$SPAD/src/input richexponential.input

Albert Rich and Timothy Daly

December 3, 2016

Abstract

Contents

2

— * —

)set break resume
)sys rm -f richexponential.output
)spool richexponential.output
)set message auto off
)clear all
--S 1 of 578
t0000:= exp(1)^(a+b*x)/x
--R
--R
--R          b x + a
--R        %e
--R   (1)  ---------
--R            x
--R                                                    Type: Expression(Integer)
--E 1
--S 2 of 578
r0000:= exp(a)*Ei(b*x)
--R
--R
--R                 a
--R   (2)  Ei(b x)%e
--R                                                    Type: Expression(Integer)
--E 2
--S 3 of 578
a0000:= integrate(t0000,x)
--R
--R
--R           x   %A b + a
--R         ++  %e
--R   (3)   |   ---------- d%A
--R        ++       %A
--R                                         Type: Union(Expression(Integer),...)
--E 3
--S 4 of 578
m0000:= a0000-r0000
--R
--R
--R           x   %A b + a
--R         ++  %e                         a
--R   (4)   |   ---------- d%A  - Ei(b x)%e
--R        ++       %A
--R                                                    Type: Expression(Integer)
--E 4

--S 5 of 578
d0000:= D(m0000,x)
--R
--R
--R          b x + a     a  b x
--R        %e        - %e %e
--R   (5)  --------------------
--R                  x
--R                                                    Type: Expression(Integer)
--E 5
--S 6 of 578
t0001:= x^3*exp((a+b*x)^3)
--R
--R
--R             3 3       2 2     2       3
--R         3  b x  + 3a b x  + 3a b x + a
--R   (6)  x %e
--R                                                    Type: Expression(Integer)
--E 6
--S 7 of 578
r0001:= -2/3*a*exp((a+b*x)^3)/b^4+1/3*exp((a+b*x)^3)*x/b^3+_
        1/9*(1+3*a^3)*(a+b*x)*Gamma(1/3,-(a+b*x)^3)/b^4/(-(a+b*x)^3)^(1/3)_
        -a^2*(a+b*x)^2*Gamma(2/3,-(a+b*x)^3)/b^4/(-(a+b*x)^3)^(2/3)
--R
--R
--R   (7)
--R                       3 3       2 2     2       3
--R                      b x  + 3a b x  + 3a b x + a
--R         (3b x - 6a)%e
--R      *
--R          +------------------------------+2
--R         3|   3 3       2 2     2       3
--R         \|- b x  - 3a b x  - 3a b x - a
--R     +
--R             3             4      _1    3 3       2 2     2       3
--R         ((3a  + 1)b x + 3a  + a)| (-,- b x  - 3a b x  - 3a b x - a )
--R                                    3
--R      *
--R          +------------------------------+
--R         3|   3 3       2 2     2       3
--R         \|- b x  - 3a b x  - 3a b x - a
--R     +
--R            2 2 2      3        4  _2    3 3       2 2     2       3
--R       (- 9a b x  - 18a b x - 9a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                                     3
--R  /
--R          +------------------------------+2

--R       4 3|   3 3       2 2     2       3
--R     9b  \|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 7
--S 8 of 578
a0001:= integrate(t0001,x)
--R
--R
--R           x        3 3      2   2        2     3
--R         ++    3  %A b  + 3%A a b  + 3%A a b + a
--R   (8)   |   %A %e                               d%A
--R        ++
--R                                         Type: Union(Expression(Integer),...)
--E 8
--S 9 of 578
m0001:= a0001-r0001
--R
--R
--R   (9)
--R              +------------------------------+2
--R           4 3|   3 3       2 2     2       3
--R         9b  \|- b x  - 3a b x  - 3a b x - a
--R      *
--R            x        3 3      2   2        2     3
--R          ++    3  %A b  + 3%A a b  + 3%A a b + a
--R          |   %A %e                               d%A
--R         ++
--R     +
--R                         3 3       2 2     2       3
--R                        b x  + 3a b x  + 3a b x + a
--R         (- 3b x + 6a)%e
--R      *
--R          +------------------------------+2
--R         3|   3 3       2 2     2       3
--R         \|- b x  - 3a b x  - 3a b x - a
--R     +
--R               3             4      _1    3 3       2 2     2       3
--R         ((- 3a  - 1)b x - 3a  - a)| (-,- b x  - 3a b x  - 3a b x - a )
--R                                      3
--R      *
--R          +------------------------------+
--R         3|   3 3       2 2     2       3
--R         \|- b x  - 3a b x  - 3a b x - a
--R     +
--R          2 2 2      3        4  _2    3 3       2 2     2       3
--R       (9a b x  + 18a b x + 9a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                                   3
--R  /

--R          +------------------------------+2
--R       4 3|   3 3       2 2     2       3
--R     9b  \|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 9
--S 10 of 578
d0001:= D(m0001,x)
--R
--R
--R   (10)  0
--R                                                    Type: Expression(Integer)
--E 10
--S 11 of 578
t0002:= x^2*exp((a+b*x)^3)
--R
--R
--R              3 3       2 2     2       3
--R          2  b x  + 3a b x  + 3a b x + a
--R   (11)  x %e
--R                                                    Type: Expression(Integer)
--E 11
--S 12 of 578
r0002:= 1/3*exp((a+b*x)^3)/b^3-1/3*a^2*(a+b*x)*_
        Gamma(1/3,-(a+b*x)^3)/b^3/(-(a+b*x)^3)^(1/3)+2/3*a*(a+b*x)^2*_
        Gamma(2/3,-(a+b*x)^3)/b^3/(-(a+b*x)^3)^(2/3)
--R
--R
--R   (12)
--R          3 3       2 2     2       3  +------------------------------+2
--R         b x  + 3a b x  + 3a b x + a  3|   3 3       2 2     2       3
--R       %e                             \|- b x  - 3a b x  - 3a b x - a
--R     +
--R             2       3  _1    3 3       2 2     2       3
--R         (- a b x - a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                          3
--R      *
--R          +------------------------------+
--R         3|   3 3       2 2     2       3
--R         \|- b x  - 3a b x  - 3a b x - a
--R     +
--R            2 2     2        3  _2    3 3       2 2     2       3
--R       (2a b x  + 4a b x + 2a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                                  3
--R  /
--R          +------------------------------+2
--R       3 3|   3 3       2 2     2       3
--R     3b  \|- b x  - 3a b x  - 3a b x - a

--R                                                    Type: Expression(Integer)
--E 12
--S 13 of 578
a0002:= integrate(t0002,x)
--R
--R
--R            x        3 3      2   2        2     3
--R          ++    2  %A b  + 3%A a b  + 3%A a b + a
--R   (13)   |   %A %e                               d%A
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 13
--S 14 of 578
m0002:= a0002-r0002
--R
--R
--R   (14)
--R              +------------------------------+2
--R           3 3|   3 3       2 2     2       3
--R         3b  \|- b x  - 3a b x  - 3a b x - a
--R      *
--R            x        3 3      2   2        2     3
--R          ++    2  %A b  + 3%A a b  + 3%A a b + a
--R          |   %A %e                               d%A
--R         ++
--R     +
--R            3 3       2 2     2       3  +------------------------------+2
--R           b x  + 3a b x  + 3a b x + a  3|   3 3       2 2     2       3
--R       - %e                             \|- b x  - 3a b x  - 3a b x - a
--R     +
--R           2       3  _1    3 3       2 2     2       3
--R         (a b x + a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                        3
--R      *
--R          +------------------------------+
--R         3|   3 3       2 2     2       3
--R         \|- b x  - 3a b x  - 3a b x - a
--R     +
--R              2 2     2        3  _2    3 3       2 2     2       3
--R       (- 2a b x  - 4a b x - 2a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                                    3
--R  /
--R          +------------------------------+2
--R       3 3|   3 3       2 2     2       3
--R     3b  \|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 14

--S 15 of 578
d0002:= D(m0002,x)
--R
--R
--R   (15)  0
--R                                                    Type: Expression(Integer)
--E 15
--S 16 of 578
t0003:= x*exp((a+b*x)^3)
--R
--R
--R              3 3       2 2     2       3
--R             b x  + 3a b x  + 3a b x + a
--R   (16)  x %e
--R                                                    Type: Expression(Integer)
--E 16
--S 17 of 578
r0003:= 1/3*a*(a+b*x)*_
        Gamma(1/3,-(a+b*x)^3)/b^2/(-(a+b*x)^3)^(1/3)-1/3*(a+b*x)^2*_
        Gamma(2/3,-(a+b*x)^3)/b^2/(-(a+b*x)^3)^(2/3)
--R
--R
--R   (17)
--R                   2  _1    3 3       2 2     2       3
--R         (a b x + a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                        3
--R      *
--R          +------------------------------+
--R         3|   3 3       2 2     2       3
--R         \|- b x  - 3a b x  - 3a b x - a
--R     +
--R           2 2             2  _2    3 3       2 2     2       3
--R       (- b x  - 2a b x - a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                                3
--R  /
--R          +------------------------------+2
--R       2 3|   3 3       2 2     2       3
--R     3b  \|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 17
--S 18 of 578
a0003:= integrate(t0003,x)
--R
--R
--R            x        3 3      2   2        2     3
--R          ++       %A b  + 3%A a b  + 3%A a b + a
--R   (18)   |   %A %e                               d%A

--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 18
--S 19 of 578
m0003:= a0003-r0003
--R
--R
--R   (19)
--R              +------------------------------+2
--R           2 3|   3 3       2 2     2       3
--R         3b  \|- b x  - 3a b x  - 3a b x - a
--R      *
--R            x        3 3      2   2        2     3
--R          ++       %A b  + 3%A a b  + 3%A a b + a
--R          |   %A %e                               d%A
--R         ++
--R     +
--R                     2  _1    3 3       2 2     2       3
--R         (- a b x - a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                          3
--R      *
--R          +------------------------------+
--R         3|   3 3       2 2     2       3
--R         \|- b x  - 3a b x  - 3a b x - a
--R     +
--R         2 2             2  _2    3 3       2 2     2       3
--R       (b x  + 2a b x + a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                              3
--R  /
--R          +------------------------------+2
--R       2 3|   3 3       2 2     2       3
--R     3b  \|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 19
--S 20 of 578
d0003:= D(m0003,x)
--R
--R
--R   (20)  0
--R                                                    Type: Expression(Integer)
--E 20
--S 21 of 578
t0004:= exp((a+b*x)^3)
--R
--R
--R            3 3       2 2     2       3
--R           b x  + 3a b x  + 3a b x + a

--R   (21)  %e
--R                                                    Type: Expression(Integer)
--E 21
--S 22 of 578
r0004:= -1/3*(a+b*x)*Gamma(1/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(1/3)
--R
--R
--R                     _1    3 3       2 2     2       3
--R         (- b x - a)| (-,- b x  - 3a b x  - 3a b x - a )
--R                       3
--R   (22)  -----------------------------------------------
--R                  +------------------------------+
--R                 3|   3 3       2 2     2       3
--R               3b\|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 22
--S 23 of 578
a0004:= integrate(t0004,x)
--R
--R
--R            x     3 3      2   2        2     3
--R          ++    %A b  + 3%A a b  + 3%A a b + a
--R   (23)   |   %e                               d%A
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 23
--S 24 of 578
m0004:= a0004-r0004
--R
--R
--R   (24)
--R            +------------------------------+
--R           3|   3 3       2 2     2       3
--R         3b\|- b x  - 3a b x  - 3a b x - a
--R      *
--R            x     3 3      2   2        2     3
--R          ++    %A b  + 3%A a b  + 3%A a b + a
--R          |   %e                               d%A
--R         ++
--R     +
--R                 _1    3 3       2 2     2       3
--R       (b x + a)| (-,- b x  - 3a b x  - 3a b x - a )
--R                   3
--R  /
--R        +------------------------------+
--R       3|   3 3       2 2     2       3
--R     3b\|- b x  - 3a b x  - 3a b x - a

--S 25 of 578
d0004:= D(m0004,x)
--R
--R
--R   (25)  0
--R                                                    Type: Expression(Integer)
--E 25
--S 26 of 578
t0005:= exp(1)^(a+b*x)/(a+b*x)
--R
--R
--R           b x + a
--R         %e
--R   (26)  ---------
--R          b x + a
--R                                                    Type: Expression(Integer)
--E 26
--S 27 of 578
r0005:= Ei(a+b*x)/b
--R
--R
--R         Ei(b x + a)
--R   (27)  -----------
--R              b
--R                                                    Type: Expression(Integer)
--E 27
--S 28 of 578
a0005:= integrate(t0005,x)
--R
--R
--R         Ei(b x + a)
--R   (28)  -----------
--R              b
--R                                         Type: Union(Expression(Integer),...)
--E 28
--S 29 of 578
m0005:= a0005-r0005
--R
--R
--R   (29)  0
--R                                                    Type: Expression(Integer)
--E 29

--S 30 of 578
d0005:= D(m0005,x)
--R
--R
--R   (30)  0
--R                                                    Type: Expression(Integer)
--E 30
--S 31 of 578
t0006:= exp((a+b*x)^3)*(a+b*x)^3
--R
--R
--R                                          3 3       2 2     2       3
--R           3 3       2 2     2       3   b x  + 3a b x  + 3a b x + a
--R   (31)  (b x  + 3a b x  + 3a b x + a )%e
--R                                                    Type: Expression(Integer)
--E 31
--S 32 of 578
r0006:= 1/3*exp((a+b*x)^3)*(a+b*x)/b+1/9*(a+b*x)*_
        Gamma(1/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(1/3)
--R
--R
--R   (32)
--R                       3 3       2 2     2       3
--R                      b x  + 3a b x  + 3a b x + a
--R         (3b x + 3a)%e
--R      *
--R          +------------------------------+
--R         3|   3 3       2 2     2       3
--R         \|- b x  - 3a b x  - 3a b x - a
--R     +
--R                 _1    3 3       2 2     2       3
--R       (b x + a)| (-,- b x  - 3a b x  - 3a b x - a )
--R                   3
--R  /
--R        +------------------------------+
--R       3|   3 3       2 2     2       3
--R     9b\|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 32
--S 33 of 578
a0006:= integrate(t0006,x)
--R
--R
--R   (33)
--R      x                                      3 3      2   2        2     3
--R    ++     3 3      2   2        2     3   %A b  + 3%A a b  + 3%A a b + a
--R    |   (%A b  + 3%A a b  + 3%A a b + a )%e                               d%A

--S 34 of 578
m0006:= a0006-r0006
--R
--R
--R   (34)
--R            +------------------------------+
--R           3|   3 3       2 2     2       3
--R         9b\|- b x  - 3a b x  - 3a b x - a
--R      *
--R         INTSIGN
--R        ,
--R            x
--R        ,
--R                                                   3 3      2   2        2     3
--R                 3 3      2   2        2     3   %A b  + 3%A a b  + 3%A a b + a
--R              (%A b  + 3%A a b  + 3%A a b + a )%e
--R           *
--R              d%A
--R     +
--R                         3 3       2 2     2       3
--R                        b x  + 3a b x  + 3a b x + a
--R         (- 3b x - 3a)%e
--R      *
--R          +------------------------------+
--R         3|   3 3       2 2     2       3
--R         \|- b x  - 3a b x  - 3a b x - a
--R     +
--R                   _1    3 3       2 2     2       3
--R       (- b x - a)| (-,- b x  - 3a b x  - 3a b x - a )
--R                     3
--R  /
--R        +------------------------------+
--R       3|   3 3       2 2     2       3
--R     9b\|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 34
--S 35 of 578
d0006:= D(m0006,x)
--R
--R
--R   (35)  0
--R                                                    Type: Expression(Integer)
--E 35
--S 36 of 578

t0007:= exp((a+b*x)^3)*(a+b*x)
--R
--R
--R                     3 3       2 2     2       3
--R                    b x  + 3a b x  + 3a b x + a
--R   (36)  (b x + a)%e
--R                                                    Type: Expression(Integer)
--E 36
--S 37 of 578
r0007:= -1/3*(a+b*x)^2*Gamma(2/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(2/3)
--R
--R
--R             2 2             2  _2    3 3       2 2     2       3
--R         (- b x  - 2a b x - a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                                  3
--R   (37)  ----------------------------------------------------------
--R                        +------------------------------+2
--R                       3|   3 3       2 2     2       3
--R                    3b \|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 37
--S 38 of 578
a0007:= integrate(t0007,x)
--R
--R
--R            x               3 3      2   2        2     3
--R          ++              %A b  + 3%A a b  + 3%A a b + a
--R   (38)   |   (%A b + a)%e                               d%A
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 38
--S 39 of 578
m0007:= a0007-r0007
--R
--R
--R   (39)
--R             +------------------------------+2
--R            3|   3 3       2 2     2       3
--R         3b \|- b x  - 3a b x  - 3a b x - a
--R      *
--R            x               3 3      2   2        2     3
--R          ++              %A b  + 3%A a b  + 3%A a b + a
--R          |   (%A b + a)%e                               d%A
--R         ++
--R     +
--R         2 2             2  _2    3 3       2 2     2       3
--R       (b x  + 2a b x + a )| (-,- b x  - 3a b x  - 3a b x - a )

--R                              3
--R  /
--R         +------------------------------+2
--R        3|   3 3       2 2     2       3
--R     3b \|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 39
--S 40 of 578
d0007:= D(m0007,x)
--R
--R
--R   (40)  0
--R                                                    Type: Expression(Integer)
--E 40
--S 41 of 578
t0008:= exp((a+b*x)^3)/(a+b*x)
--R
--R
--R            3 3       2 2     2       3
--R           b x  + 3a b x  + 3a b x + a
--R         %e
--R   (41)  ------------------------------
--R                     b x + a
--R                                                    Type: Expression(Integer)
--E 41
--S 42 of 578
r0008:= 1/3*Ei((a+b*x)^3)/b
--R
--R
--R             3 3       2 2     2       3
--R         Ei(b x  + 3a b x  + 3a b x + a )
--R   (42)  --------------------------------
--R                        3b
--R                                                    Type: Expression(Integer)
--E 42
--S 43 of 578
a0008:= integrate(t0008,x)
--R
--R
--R             3 3       2 2     2       3
--R         Ei(b x  + 3a b x  + 3a b x + a )
--R   (43)  --------------------------------
--R                        3b
--R                                         Type: Union(Expression(Integer),...)
--E 43

--S 44 of 578
m0008:= a0008-r0008
--R
--R
--R   (44)  0
--R                                                    Type: Expression(Integer)
--E 44
--S 45 of 578
d0008:= D(m0008,x)
--R
--R
--R   (45)  0
--R                                                    Type: Expression(Integer)
--E 45
--S 46 of 578
t0009:= exp((a+b*x)^3)/(a+b*x)^2
--R
--R
--R            3 3       2 2     2       3
--R           b x  + 3a b x  + 3a b x + a
--R         %e
--R   (46)  ------------------------------
--R                2 2             2
--R               b x  + 2a b x + a
--R                                                    Type: Expression(Integer)
--E 46
--S 47 of 578
r0009:= -exp((a+b*x)^3)/b/(a+b*x)-(a+b*x)^2*_
        Gamma(2/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(2/3)
--R
--R
--R   (47)
--R            3 3       2 2     2       3  +------------------------------+2
--R           b x  + 3a b x  + 3a b x + a  3|   3 3       2 2     2       3
--R       - %e                             \|- b x  - 3a b x  - 3a b x - a
--R     +
--R           3 3       2 2     2       3  _2    3 3       2 2     2       3
--R       (- b x  - 3a b x  - 3a b x - a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                                          3
--R  /
--R                 +------------------------------+2
--R       2        3|   3 3       2 2     2       3
--R     (b x + a b)\|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 47
--S 48 of 578

a0009:= integrate(t0009,x)
--R
--R
--R                  3 3      2   2        2     3
--R            x   %A b  + 3%A a b  + 3%A a b + a
--R          ++  %e
--R   (48)   |   --------------------------------- d%A
--R         ++            2 2              2
--R                     %A b  + 2%A a b + a
--R                                         Type: Union(Expression(Integer),...)
--E 48
--S 49 of 578
m0009:= a0009-r0009
--R
--R
--R   (49)
--R                     +------------------------------+2
--R           2        3|   3 3       2 2     2       3
--R         (b x + a b)\|- b x  - 3a b x  - 3a b x - a
--R      *
--R                  3 3      2   2        2     3
--R            x   %A b  + 3%A a b  + 3%A a b + a
--R          ++  %e
--R          |   --------------------------------- d%A
--R         ++            2 2              2
--R                     %A b  + 2%A a b + a
--R     +
--R          3 3       2 2     2       3  +------------------------------+2
--R         b x  + 3a b x  + 3a b x + a  3|   3 3       2 2     2       3
--R       %e                             \|- b x  - 3a b x  - 3a b x - a
--R     +
--R         3 3       2 2     2       3  _2    3 3       2 2     2       3
--R       (b x  + 3a b x  + 3a b x + a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                                        3
--R  /
--R                 +------------------------------+2
--R       2        3|   3 3       2 2     2       3
--R     (b x + a b)\|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 49
--S 50 of 578
d0009:= D(m0009,x)
--R
--R
--R   (50)  0
--R                                                    Type: Expression(Integer)
--E 50

--S 51 of 578
t0010:= exp((a+b*x)^3)/(a+b*x)^3
--R
--R
--R            3 3       2 2     2       3
--R           b x  + 3a b x  + 3a b x + a
--R         %e
--R   (51)  ------------------------------
--R           3 3       2 2     2       3
--R          b x  + 3a b x  + 3a b x + a
--R                                                    Type: Expression(Integer)
--E 51
--S 52 of 578
r0010:= -1/2*exp((a+b*x)^3)/b/(a+b*x)^2-1/2*(a+b*x)*_
        Gamma(1/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(1/3)
--R
--R
--R   (52)
--R            3 3       2 2     2       3  +------------------------------+
--R           b x  + 3a b x  + 3a b x + a  3|   3 3       2 2     2       3
--R       - %e                             \|- b x  - 3a b x  - 3a b x - a
--R     +
--R           3 3       2 2     2       3  _1    3 3       2 2     2       3
--R       (- b x  - 3a b x  - 3a b x - a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                                          3
--R  /
--R                             +------------------------------+
--R        3 2       2      2  3|   3 3       2 2     2       3
--R     (2b x  + 4a b x + 2a b)\|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 52
--S 53 of 578
a0010:= integrate(t0010,x)
--R
--R
--R                  3 3      2   2        2     3
--R            x   %A b  + 3%A a b  + 3%A a b + a
--R          ++  %e
--R   (53)   |   --------------------------------- d%A
--R         ++      3 3      2   2        2     3
--R               %A b  + 3%A a b  + 3%A a b + a
--R                                         Type: Union(Expression(Integer),...)
--E 53
--S 54 of 578
m0010:= a0010-r0010
--R
--R

--R   (54)
--R                                 +------------------------------+
--R            3 2       2      2  3|   3 3       2 2     2       3
--R         (2b x  + 4a b x + 2a b)\|- b x  - 3a b x  - 3a b x - a
--R      *
--R                  3 3      2   2        2     3
--R            x   %A b  + 3%A a b  + 3%A a b + a
--R          ++  %e
--R          |   --------------------------------- d%A
--R         ++      3 3      2   2        2     3
--R               %A b  + 3%A a b  + 3%A a b + a
--R     +
--R          3 3       2 2     2       3  +------------------------------+
--R         b x  + 3a b x  + 3a b x + a  3|   3 3       2 2     2       3
--R       %e                             \|- b x  - 3a b x  - 3a b x - a
--R     +
--R         3 3       2 2     2       3  _1    3 3       2 2     2       3
--R       (b x  + 3a b x  + 3a b x + a )| (-,- b x  - 3a b x  - 3a b x - a )
--R                                        3
--R  /
--R                             +------------------------------+
--R        3 2       2      2  3|   3 3       2 2     2       3
--R     (2b x  + 4a b x + 2a b)\|- b x  - 3a b x  - 3a b x - a
--R                                                    Type: Expression(Integer)
--E 54
--S 55 of 578
d0010:= D(m0010,x)
--R
--R
--R   (55)  0
--R                                                    Type: Expression(Integer)
--E 55
--S 56 of 578
t0011:= x^m*exp(1)^(x^n)
--R
--R
--R              n
--R          m  x
--R   (56)  x %e
--R                                                    Type: Expression(Integer)
--E 56
--S 57 of 578
r0011:= -x^(1+m)*Gamma((1+m)/n,-x^n)*(-x^n)^(-(1+m)/n)/n
--R
--R
--R                       - m - 1
--R                       -------

--R            m + 1    n    n    _m + 1    n
--R           x     (- x )       | (-----,- x )
--R                                   n
--R   (57)  - ---------------------------------
--R                           n
--R                                                    Type: Expression(Integer)
--E 57
--S 58 of 578
a0011:= integrate(t0011,x)
--R
--R
--R            x        n
--R          ++    m  %A
--R   (58)   |   %A %e   d%A
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 58
--S 59 of 578
m0011:= a0011-r0011
--R
--R
--R                                          - m - 1
--R             x        n                   -------
--R           ++    m  %A         m + 1    n    n    _m + 1    n
--R         n |   %A %e   d%A  + x     (- x )       | (-----,- x )
--R          ++                                          n
--R   (59)  ------------------------------------------------------
--R                                    n
--R                                                    Type: Expression(Integer)
--E 59
--S 60 of 578
d0011:= D(m0011,x)
--R
--R
--R   (60)
--R                         - m - 1                            - n - m - 1
--R                         -------                            -----------
--R                  m    n    n              m + 1 n - 1    n      n
--R         ((m + 1)x (- x )        + (m + 1)x     x     (- x )           )
--R      *
--R          _m + 1    n
--R         | (-----,- x )
--R              n
--R     +
--R                               - n + m + 1      - m - 1
--R                        n      -----------      -------          n
--R          m + 1 n - 1  x     n      n         n    n         m  x

--R       n x     x     %e  (- x )           (- x )        + n x %e
--R  /
--R     n
--R                                                    Type: Expression(Integer)
--E 60
--S 61 of 578
t0012:= x^m*f^(x^n)
--R
--R
--R             n
--R          m x
--R   (61)  x f
--R                                                    Type: Expression(Integer)
--E 61
--S 62 of 578
r0012:= -x^(1+m)*Gamma((1+m)/n,-x^n*log(f))*(-x^n*log(f))^(-(1+m)/n)/n
--R
--R
--R                             - m - 1
--R                             -------
--R            m + 1          n    n    _m + 1          n
--R           x     (- log(f)x )       | (-----,- log(f)x )
--R                                         n
--R   (62)  - ---------------------------------------------
--R                                 n
--R                                                    Type: Expression(Integer)
--E 62
--S 63 of 578
a0012:= integrate(t0012,x)
--R
--R
--R            x       n
--R          ++    m %A
--R   (63)   |   %A f   d%A
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 63
--S 64 of 578
m0012:= a0012-r0012
--R
--R
--R                                               - m - 1
--R             x       n                         -------
--R           ++    m %A         m + 1          n    n    _m + 1          n
--R         n |   %A f   d%A  + x     (- log(f)x )       | (-----,- log(f)x )
--R          ++                                               n

--R   (64)  -----------------------------------------------------------------
--R                                         n
--R                                                    Type: Expression(Integer)
--E 64
--S 65 of 578
d0012:= D(m0012,x)
--R
--R
--R   (65)
--R                                - m - 1
--R                                -------
--R                   m          n    n
--R           (m + 1)x (- log(f)x )
--R         +
--R                                                - n - m - 1
--R                                                -----------
--R                         m + 1 n - 1          n      n
--R           (m + 1)log(f)x     x     (- log(f)x )
--R      *
--R          _m + 1          n
--R         | (-----,- log(f)x )
--R              n
--R     +
--R             n
--R          m x
--R       n x f
--R     +
--R                                                 - n + m + 1            - m - 1
--R                                    n            -----------            -------
--R                m + 1 n - 1  log(f)x           n      n               n    n
--R       n log(f)x     x     %e        (- log(f)x )           (- log(f)x )
--R  /
--R     n
--R                                                    Type: Expression(Integer)
--E 65
--S 66 of 578
t0013:= (a+b*x)^m*exp(1)^((a+b*x)^n)
--R
--R
--R                              n
--R                  m  (b x + a)
--R   (66)  (b x + a) %e
--R                                                    Type: Expression(Integer)
--E 66
--S 67 of 578
r0013:= -(a+b*x)^(1+m)*Gamma((1+m)/n,-(a+b*x)^n)*(-(a+b*x)^n)^(-(1+m)/n)/b/n
--R

--R
--R                                       - m - 1
--R                                       -------
--R                    m + 1            n    n    _m + 1            n
--R           (b x + a)     (- (b x + a) )       | (-----,- (b x + a) )
--R                                                   n
--R   (67)  - ---------------------------------------------------------
--R                                      b n
--R                                                    Type: Expression(Integer)
--E 67
--S 68 of 578
a0013:= integrate(t0013,x)
--R
--R
--R            x                        n
--R          ++            m  (%A b + a)
--R   (68)   |   (%A b + a) %e           d%A
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 68
--S 69 of 578
m0013:= a0013-r0013
--R
--R
--R   (69)
--R             x                        n
--R           ++            m  (%A b + a)
--R       b n |   (%A b + a) %e           d%A
--R          ++
--R     +
--R                                   - m - 1
--R                                   -------
--R                m + 1            n    n    _m + 1            n
--R       (b x + a)     (- (b x + a) )       | (-----,- (b x + a) )
--R                                               n
--R  /
--R     b n
--R                                                    Type: Expression(Integer)
--E 69
--S 70 of 578
d0013:= D(m0013,x)
--R
--R
--R   (70)
--R                                          - m - 1
--R                                          -------
--R                           m            n    n

--R           (m + 1)(b x + a) (- (b x + a) )
--R         +
--R                                                            - n - m - 1
--R                                                            -----------
--R                           m + 1         n - 1            n      n
--R           (m + 1)(b x + a)     (b x + a)     (- (b x + a) )
--R      *
--R          _m + 1            n
--R         | (-----,- (b x + a) )
--R              n
--R     +
--R                                                                 - n + m + 1
--R                                                  n              -----------
--R                    m + 1         n - 1  (b x + a)             n      n
--R         n (b x + a)     (b x + a)     %e          (- (b x + a) )
--R      *
--R                       - m - 1
--R                       -------
--R                     n    n
--R         (- (b x + a) )
--R     +
--R                              n
--R                  m  (b x + a)
--R       n (b x + a) %e
--R  /
--R     n
--R                                                    Type: Expression(Integer)
--E 70
--S 71 of 578
t0014:= (a+b*x)^m*f^((a+b*x)^n)
--R
--R
--R                             n
--R                  m (b x + a)
--R   (71)  (b x + a) f
--R                                                    Type: Expression(Integer)
--E 71
--S 72 of 578
r0014:= -(a+b*x)^(1+m)*_
        Gamma((1+m)/n,-(a+b*x)^n*log(f))*(-(a+b*x)^n*log(f))^(-(1+m)/n)/b/n
--R
--R
--R   (72)
--R                                       - m - 1
--R                                       -------
--R              m + 1                  n    n    _m + 1                  n
--R     (b x + a)     (- log(f)(b x + a) )       | (-----,- log(f)(b x + a) )
--R                                                   n

--R   - ---------------------------------------------------------------------
--R                                      b n
--R                                                    Type: Expression(Integer)
--E 72
--S 73 of 578
a0014:= integrate(t0014,x)
--R
--R
--R            x                       n
--R          ++            m (%A b + a)
--R   (73)   |   (%A b + a) f           d%A
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 73
--S 74 of 578
m0014:= a0014-r0014
--R
--R
--R   (74)
--R             x                       n
--R           ++            m (%A b + a)
--R       b n |   (%A b + a) f           d%A
--R          ++
--R     +
--R                                         - m - 1
--R                                         -------
--R                m + 1                  n    n    _m + 1                  n
--R       (b x + a)     (- log(f)(b x + a) )       | (-----,- log(f)(b x + a) )
--R                                                     n
--R  /
--R     b n
--R                                                    Type: Expression(Integer)
--E 74
--S 75 of 578
d0014:= D(m0014,x)
--R
--R
--R   (75)
--R                                                - m - 1
--R                                                -------
--R                           m                  n    n
--R           (m + 1)(b x + a) (- log(f)(b x + a) )
--R         +
--R                                   m + 1         n - 1
--R             (m + 1)log(f)(b x + a)     (b x + a)
--R          *
--R                                 - n - m - 1

--R                                 -----------
--R                               n      n
--R             (- log(f)(b x + a) )
--R      *
--R          _m + 1                  n
--R         | (-----,- log(f)(b x + a) )
--R              n
--R     +
--R                             n
--R                  m (b x + a)
--R       n (b x + a) f
--R     +
--R                                                              n
--R                          m + 1         n - 1  log(f)(b x + a)
--R         n log(f)(b x + a)     (b x + a)     %e
--R      *
--R                             - n + m + 1                    - m - 1
--R                             -----------                    -------
--R                           n      n                       n    n
--R         (- log(f)(b x + a) )           (- log(f)(b x + a) )
--R  /
--R     n
--R                                                    Type: Expression(Integer)
--E 75
--S 76 of 578
t0015:= exp(1)^(c+d*x)/(a+b*x)^2
--R
--R
--R                d x + c
--R              %e
--R   (76)  ------------------
--R          2 2             2
--R         b x  + 2a b x + a
--R                                                    Type: Expression(Integer)
--E 76
--S 77 of 578
r0015:= -exp(1)^(c+d*x)/b/(a+b*x)+d*exp(1)^(c-a*d/b)*Ei(d*(a+b*x)/b)/b^2
--R
--R
--R                                                       - a d + b c
--R                                                       -----------
--R               d x + c                   b d x + a d        b
--R         - b %e        + (b d x + a d)Ei(-----------)%e
--R                                              b
--R   (77)  ---------------------------------------------------------
--R                                  3       2
--R                                 b x + a b
--R                                                    Type: Expression(Integer)

--E 77
--S 78 of 578
a0015:= integrate(t0015,x)
--R
--R
--R            x        %A d + c
--R          ++       %e
--R   (78)   |   -------------------- d%A
--R         ++     2 2              2
--R              %A b  + 2%A a b + a
--R                                         Type: Union(Expression(Integer),...)
--E 78
--S 79 of 578
m0015:= a0015-r0015
--R
--R
--R   (79)
--R                      x        %A d + c
--R         3       2  ++       %e                         d x + c
--R       (b x + a b ) |   -------------------- d%A  + b %e
--R                   ++     2 2              2
--R                        %A b  + 2%A a b + a
--R     +
--R                                       - a d + b c
--R                                       -----------
--R                         b d x + a d        b
--R       (- b d x - a d)Ei(-----------)%e
--R                              b
--R  /
--R      3       2
--R     b x + a b
--R                                                    Type: Expression(Integer)
--E 79
--S 80 of 578
d0015:= D(m0015,x)
--R
--R
--R               - a d + b c  b d x + a d
--R               -----------  -----------
--R                    b            b            d x + c
--R         - d %e           %e            + d %e
--R   (80)  --------------------------------------------
--R                            2
--R                           b x + a b
--R                                                    Type: Expression(Integer)
--E 80

--S 81 of 578
t0016:= exp(1)^(c+d*x)/(a+b*x)^3
--R
--R
--R                     d x + c
--R                   %e
--R   (81)  ----------------------------
--R          3 3       2 2     2       3
--R         b x  + 3a b x  + 3a b x + a
--R                                                    Type: Expression(Integer)
--E 81
--S 82 of 578
r0016:= -1/2*exp(1)^(c+d*x)/b/(a+b*x)^2-1/2*d*_
        exp(1)^(c+d*x)/b^2/(a+b*x)+1/2*d^2*exp(1)^(c-a*d/b)*_
        Ei(d*(a+b*x)/b)/b^3
--R
--R
--R   (82)
--R           2               2   d x + c
--R       (- b d x - a b d - b )%e
--R     +
--R                                                  - a d + b c
--R                                                  -----------
--R         2 2 2         2     2 2    b d x + a d        b
--R       (b d x  + 2a b d x + a d )Ei(-----------)%e
--R                                         b
--R  /
--R       5 2       4      2 3
--R     2b x  + 4a b x + 2a b
--R                                                    Type: Expression(Integer)
--E 82
--S 83 of 578
a0016:= integrate(t0016,x)
--R
--R
--R            x              %A d + c
--R          ++             %e
--R   (83)   |   ------------------------------- d%A
--R         ++     3 3      2   2        2     3
--R              %A b  + 3%A a b  + 3%A a b + a
--R                                         Type: Union(Expression(Integer),...)
--E 83
--S 84 of 578
m0016:= a0016-r0016
--R
--R
--R   (84)

--R                                  x              %A d + c
--R          5 2       4      2 3  ++             %e
--R       (2b x  + 4a b x + 2a b ) |   ------------------------------- d%A
--R                               ++     3 3      2   2        2     3
--R                                    %A b  + 3%A a b  + 3%A a b + a
--R     +
--R         2               2   d x + c
--R       (b d x + a b d + b )%e
--R     +
--R                                                    - a d + b c
--R                                                    -----------
--R           2 2 2         2     2 2    b d x + a d        b
--R       (- b d x  - 2a b d x - a d )Ei(-----------)%e
--R                                           b
--R  /
--R       5 2       4      2 3
--R     2b x  + 4a b x + 2a b
--R                                                    Type: Expression(Integer)
--E 84
--S 85 of 578
d0016:= D(m0016,x)
--R
--R
--R               - a d + b c  b d x + a d
--R               -----------  -----------
--R            2       b            b         2  d x + c
--R         - d %e           %e            + d %e
--R   (85)  --------------------------------------------
--R                           3        2
--R                         2b x + 2a b
--R                                                    Type: Expression(Integer)
--E 85
--S 86 of 578
t0017:= exp((c+d*x)^2)*(a+b*x)^2
--R
--R
--R                                2 2             2
--R           2 2             2   d x  + 2c d x + c
--R   (86)  (b x  + 2a b x + a )%e
--R                                                    Type: Expression(Integer)
--E 86
--S 87 of 578
r0017:= -b*(1/2*b*c-a*d)*_
        exp((c+d*x)^2)/d^3+1/2*b^2*_
        exp((c+d*x)^2)*x/d^2-1/4*(b^2*(1-2*c^2)+4*a*b*c*d-2*a^2*d^2)*_
        %pi^(1/2)*erfi(c+d*x)/d^3
--R

--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 87
--S 88 of 578
a0017:= integrate(t0017,x)
--R
--R
--R            x                           2 2              2
--R          ++     2 2              2   %A d  + 2%A c d + c
--R   (87)   |   (%A b  + 2%A a b + a )%e                    d%A
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 88
--S 89 of 578
m0017:= a0017-r0017
--R
--R
--R            x                           2 2              2
--R          ++     2 2              2   %A d  + 2%A c d + c
--R   (88)   |   (%A b  + 2%A a b + a )%e                    d%A  - r0017
--R         ++
--R                                                    Type: Expression(Integer)
--E 89
--S 90 of 578
d0017:= D(m0017,x)
--R
--R
--R                                2 2             2
--R           2 2             2   d x  + 2c d x + c
--R   (89)  (b x  + 2a b x + a )%e
--R                                                    Type: Expression(Integer)
--E 90
--S 91 of 578
t0018:= exp((c+d*x)^3)*(a+b*x)^2
--R
--R

--R                                3 3       2 2     2       3
--R           2 2             2   d x  + 3c d x  + 3c d x + c
--R   (90)  (b x  + 2a b x + a )%e
--R                                                    Type: Expression(Integer)
--E 91
--S 92 of 578
r0018:= 1/3*b^2*exp((c+d*x)^3)/d^3-1/3*(b*c-a*d)^2*(c+d*x)*_
        Gamma(1/3,-(c+d*x)^3)/d^3/(-(c+d*x)^3)^(1/3)+_
        2/3*b*(b*c-a*d)*(c+d*x)^2*_
        Gamma(2/3,-(c+d*x)^3)/d^3/(-(c+d*x)^3)^(2/3)
--R
--R
--R   (91)
--R            3 3       2 2     2       3  +------------------------------+2
--R        2  d x  + 3c d x  + 3c d x + c  3|   3 3       2 2     2       3
--R       b %e                             \|- d x  - 3c d x  - 3c d x - c
--R     +
--R              2 3           2    2 2       2   2         2     2 3
--R         ((- a d  + 2a b c d  - b c d)x - a c d  + 2a b c d - b c )
--R      *
--R                                              +------------------------------+
--R          _1    3 3       2 2     2       3 3|   3 3       2 2     2       3
--R         | (-,- d x  - 3c d x  - 3c d x - c )\|- d x  - 3c d x  - 3c d x - c
--R            3
--R     +
--R                   3     2   2  2              2     2 2            2      2 3
--R         ((- 2a b d  + 2b c d )x  + (- 4a b c d  + 4b c d)x - 2a b c d + 2b c )
--R      *
--R          _2    3 3       2 2     2       3
--R         | (-,- d x  - 3c d x  - 3c d x - c )
--R            3
--R  /
--R          +------------------------------+2
--R       3 3|   3 3       2 2     2       3
--R     3d  \|- d x  - 3c d x  - 3c d x - c
--R                                                    Type: Expression(Integer)
--E 92
--S 93 of 578
a0018:= integrate(t0018,x)
--R
--R
--R            x                           3 3      2   2        2     3
--R          ++     2 2              2   %A d  + 3%A c d  + 3%A c d + c
--R   (92)   |   (%A b  + 2%A a b + a )%e                               d%A
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 93

--S 94 of 578
m0018:= a0018-r0018
--R
--R
--R   (93)
--R              +------------------------------+2
--R           3 3|   3 3       2 2     2       3
--R         3d  \|- d x  - 3c d x  - 3c d x - c
--R      *
--R            x                           3 3      2   2        2     3
--R          ++     2 2              2   %A d  + 3%A c d  + 3%A c d + c
--R          |   (%A b  + 2%A a b + a )%e                               d%A
--R         ++
--R     +
--R              3 3       2 2     2       3  +------------------------------+2
--R          2  d x  + 3c d x  + 3c d x + c  3|   3 3       2 2     2       3
--R       - b %e                             \|- d x  - 3c d x  - 3c d x - c
--R     +
--R            2 3           2    2 2       2   2         2     2 3
--R         ((a d  - 2a b c d  + b c d)x + a c d  - 2a b c d + b c )
--R      *
--R                                              +------------------------------+
--R          _1    3 3       2 2     2       3 3|   3 3       2 2     2       3
--R         | (-,- d x  - 3c d x  - 3c d x - c )\|- d x  - 3c d x  - 3c d x - c
--R            3
--R     +
--R                 3     2   2  2            2     2 2            2      2 3
--R         ((2a b d  - 2b c d )x  + (4a b c d  - 4b c d)x + 2a b c d - 2b c )
--R      *
--R          _2    3 3       2 2     2       3
--R         | (-,- d x  - 3c d x  - 3c d x - c )
--R            3
--R  /
--R          +------------------------------+2
--R       3 3|   3 3       2 2     2       3
--R     3d  \|- d x  - 3c d x  - 3c d x - c
--R                                                    Type: Expression(Integer)
--E 94
--S 95 of 578
d0018:= D(m0018,x)
--R
--R
--R   (94)  0
--R                                                    Type: Expression(Integer)
--E 95
--S 96 of 578
t0019:= exp((c+d*x)^3)*(a+b*x)
--R

--R
--R                     3 3       2 2     2       3
--R                    d x  + 3c d x  + 3c d x + c
--R   (95)  (b x + a)%e
--R                                                    Type: Expression(Integer)
--E 96
--S 97 of 578
r0019:= 1/3*(b*c-a*d)*(c+d*x)*_
        Gamma(1/3,-(c+d*x)^3)/d^2/(-(c+d*x)^3)^(1/3)-_
        1/3*b*(c+d*x)^2*_
        Gamma(2/3,-(c+d*x)^3)/d^2/(-(c+d*x)^3)^(2/3)
--R
--R
--R   (96)
--R                2                        2  _1    3 3       2 2     2       3
--R         ((- a d  + b c d)x - a c d + b c )| (-,- d x  - 3c d x  - 3c d x - c )
--R                                              3
--R      *
--R          +------------------------------+
--R         3|   3 3       2 2     2       3
--R         \|- d x  - 3c d x  - 3c d x - c
--R     +
--R             2 2                 2  _2    3 3       2 2     2       3
--R       (- b d x  - 2b c d x - b c )| (-,- d x  - 3c d x  - 3c d x - c )
--R                                      3
--R  /
--R          +------------------------------+2
--R       2 3|   3 3       2 2     2       3
--R     3d  \|- d x  - 3c d x  - 3c d x - c
--R                                                    Type: Expression(Integer)
--E 97
--S 98 of 578
a0019:= integrate(t0019,x)
--R
--R
--R            x               3 3      2   2        2     3
--R          ++              %A d  + 3%A c d  + 3%A c d + c
--R   (97)   |   (%A b + a)%e                               d%A
--R         ++
--R                                         Type: Union(Expression(Integer),...)
--E 98
--S 99 of 578
m0019:= a0019-r0019
--R
--R
--R   (98)
--R              +------------------------------+2

--R           2 3|   3 3       2 2     2       3
--R         3d  \|- d x  - 3c d x  - 3c d x - c
--R      *
--R            x               3 3      2   2        2     3
--R          ++              %A d  + 3%A c d  + 3%A c d + c
--R          |   (%A b + a)%e                               d%A
--R         ++
--R     +
--R              2                        2  _1    3 3       2 2     2       3
--R         ((a d  - b c d)x + a c d - b c )| (-,- d x  - 3c d x  - 3c d x - c )
--R                                            3
--R      *
--R          +------------------------------+
--R         3|   3 3       2 2     2       3
--R         \|- d x  - 3c d x  - 3c d x - c
--R     +
--R           2 2                 2  _2    3 3       2 2     2       3
--R       (b d x  + 2b c d x + b c )| (-,- d x  - 3c d x  - 3c d x - c )
--R                                    3
--R  /
--R          +------------------------------+2
--R       2 3|   3 3       2 2     2       3
--R     3d  \|- d x  - 3c d x  - 3c d x - c
--R                                                    Type: Expression(Integer)
--E 99
--S 100 of 578
d0019:= D(m0019,x)
--R
--R
--R   (99)  0
--R                                                    Type: Expression(Integer)
--E 100
--S 101 of 578
t0020:= x^2*exp(1)^(a+b*x)/(c+d*x^2)
--R
--R
--R           2  b x + a
--R          x %e
--R   (100)  -----------
--R               2
--R            d x  + c
--R                                                    Type: Expression(Integer)
--E 101
--S 102 of 578
r0020:= exp(1)^(a+b*x)/b/d-1/2*c^(1/2)*_
        exp(1)^(a+b*c^(1/2)/(-d)^(1/2))*_
        Ei(-b*(c^(1/2)-(-d)^(1/2)*x)/(-d)^(1/2))/(-d)^(3/2)+1/2*c^(1/2)*_

        exp(1)^(a-b*c^(1/2)/(-d)^(1/2))*_
        Ei(b*(c^(1/2)+(-d)^(1/2)*x)/(-d)^(1/2))/(-d)^(3/2)
--R
--R
--R   (101)
--R                                       +-+     +---+
--R                                     b\|c  + a\|- d
--R                                     ---------------
--R                   +-+       +---+         +---+
--R         +-+   - b\|c  + b x\|- d         \|- d
--R       b\|c Ei(-------------------)%e
--R                       +---+
--R                      \|- d
--R     +
--R                                         +-+     +---+
--R                                     - b\|c  + a\|- d
--R                                     -----------------
--R                   +-+       +---+          +---+
--R           +-+   b\|c  + b x\|- d          \|- d            b x + a +---+
--R       - b\|c Ei(-----------------)%e                  + 2%e       \|- d
--R                        +---+
--R                       \|- d
--R  /
--R          +---+
--R     2b d\|- d
--R                                                    Type: Expression(Integer)
--E 102
--S 103 of 578
a0020:= integrate(t0020,x)
--R
--R
--R             x   2  %A b + a
--R           ++  %A %e
--R   (102)   |   ------------- d%A
--R          ++        2
--R                  %A d + c
--R                                         Type: Union(Expression(Integer),...)
--E 103
--S 104 of 578
m0020:= a0020-r0020
--R
--R
--R   (103)
--R                    x   2  %A b + a
--R            +---+ ++  %A %e
--R       2b d\|- d  |   ------------- d%A
--R                 ++        2
--R                         %A d + c

--R     +
--R                                         +-+     +---+
--R                                       b\|c  + a\|- d
--R                                       ---------------
--R                     +-+       +---+         +---+
--R           +-+   - b\|c  + b x\|- d         \|- d
--R       - b\|c Ei(-------------------)%e
--R                         +---+
--R                        \|- d
--R     +
--R                                       +-+     +---+
--R                                   - b\|c  + a\|- d
--R                                   -----------------
--R                 +-+       +---+          +---+
--R         +-+   b\|c  + b x\|- d          \|- d            b x + a +---+
--R       b\|c Ei(-----------------)%e                  - 2%e       \|- d
--R                      +---+
--R                     \|- d
--R  /
--R          +---+
--R     2b d\|- d
--R                                                    Type: Expression(Integer)
--E 104
--S 105 of 578
d0020:= D(m0020,x)
--R
--R
--R   (104)
--R                                +-+     +---+    +-+       +---+
--R                            - b\|c  + a\|- d   b\|c  + b x\|- d
--R                            -----------------  -----------------
--R                                   +---+              +---+
--R            +---+ +-+             \|- d              \|- d
--R       (- x\|- d \|c  + c)%e                 %e
--R     +
--R                              +-+       +---+    +-+     +---+
--R                          - b\|c  + b x\|- d   b\|c  + a\|- d
--R                          -------------------  ---------------
--R                                  +---+              +---+
--R          +---+ +-+              \|- d              \|- d             b x + a
--R       (x\|- d \|c  + c)%e                   %e                - 2c %e
--R  /
--R       2 2
--R     2d x  + 2c d
--R                                                    Type: Expression(Integer)
--E 105
--S 106 of 578
t0021:= 1/(a+b*exp(1)^(c-d*x))

--R
--R
--R                  1
--R   (105)  -----------------
--R              - d x + c
--R          b %e          + a
--R                                                    Type: Expression(Integer)
--E 106
--S 107 of 578
r0021:= log(b+a*exp(-c+d*x))/a/d
--R
--R
--R                  d x - c
--R          log(a %e        + b)
--R   (106)  --------------------
--R                   a d
--R                                                    Type: Expression(Integer)
--E 107
--S 108 of 578
a0021:= integrate(t0021,x)
--R
--R
--R                  - d x + c
--R          log(b %e          + a) + d x
--R   (107)  ----------------------------
--R                       a d
--R                                         Type: Union(Expression(Integer),...)
--E 108
--S 109 of 578
m0021:= a0021-r0021
--R
--R
--R                    d x - c                - d x + c
--R          - log(a %e        + b) + log(b %e          + a) + d x
--R   (108)  -----------------------------------------------------
--R                                   a d
--R                                                    Type: Expression(Integer)
--E 109
--S 110 of 578
d0021:= D(m0021,x)
--R
--R
--R                             - d x + c  d x - c
--R                       - b %e         %e        + b
--R   (109)  -----------------------------------------------------
--R                 - d x + c    2   d x - c    2  - d x + c

--R          (a b %e          + a )%e        + b %e          + a b
--R                                                    Type: Expression(Integer)
--E 110
--S 111 of 578
t0022:= 1/(a+b*exp(1)^(c-d*x))^2
--R
--R
--R                              1
--R   (110)  ----------------------------------------
--R           2   - d x + c 2          - d x + c    2
--R          b (%e         )  + 2a b %e          + a
--R                                                    Type: Expression(Integer)
--E 111
--S 112 of 578
r0022:= -1/a/d/(a+b*exp(1)^(c-d*x))+log(b+a*exp(1)^(-c+d*x))/a^2/d
--R
--R
--R               - d x + c             d x - c
--R          (b %e          + a)log(a %e        + b) - a
--R   (111)  -------------------------------------------
--R                     2      - d x + c    3
--R                    a b d %e          + a d
--R                                                    Type: Expression(Integer)
--E 112
--S 113 of 578
a0022:= integrate(t0022,x)
--R
--R
--R   (112)
--R        - d x + c             - d x + c                - d x + c
--R   (b %e          + a)log(b %e          + a) + b d x %e          + a d x - a
--R   -------------------------------------------------------------------------
--R                             2      - d x + c    3
--R                            a b d %e          + a d
--R                                         Type: Union(Expression(Integer),...)
--E 113
--S 114 of 578
m0022:= a0022-r0022
--R
--R
--R                    d x - c                - d x + c
--R          - log(a %e        + b) + log(b %e          + a) + d x
--R   (113)  -----------------------------------------------------
--R                                    2
--R                                   a d
--R                                                    Type: Expression(Integer)

--E 114
--S 115 of 578
d0022:= D(m0022,x)
--R
--R
--R                              - d x + c  d x - c
--R                        - b %e         %e        + b
--R   (114)  -------------------------------------------------------
--R            2    - d x + c    3   d x - c      2  - d x + c    2
--R          (a b %e          + a )%e        + a b %e          + a b
--R                                                    Type: Expression(Integer)
--E 115
--S 116 of 578
t0023:= 1/(a+b*exp(1)^(-c-d*x))
--R
--R
--R                  1
--R   (115)  -----------------
--R              - d x - c
--R          b %e          + a
--R                                                    Type: Expression(Integer)
--E 116
--S 117 of 578
r0023:= log(b+a*exp(c+d*x))/a/d
--R
--R
--R                  d x + c
--R          log(a %e        + b)
--R   (116)  --------------------
--R                   a d
--R                                                    Type: Expression(Integer)
--E 117
--S 118 of 578
a0023:= integrate(t0023,x)
--R
--R
--R                  - d x - c
--R          log(b %e          + a) + d x
--R   (117)  ----------------------------
--R                       a d
--R                                         Type: Union(Expression(Integer),...)
--E 118
--S 119 of 578
m0023:= a0023-r0023
--R

--R
--R                    d x + c                - d x - c
--R          - log(a %e        + b) + log(b %e          + a) + d x
--R   (118)  -----------------------------------------------------
--R                                   a d
--R                                                    Type: Expression(Integer)
--E 119
--S 120 of 578
d0023:= D(m0023,x)
--R
--R
--R                             - d x - c  d x + c
--R                       - b %e         %e        + b
--R   (119)  -----------------------------------------------------
--R                 - d x - c    2   d x + c    2  - d x - c
--R          (a b %e          + a )%e        + b %e          + a b
--R                                                    Type: Expression(Integer)
--E 120
--S 121 of 578
t0024:= 1/(a+b*exp(1)^(-c-d*x))^2
--R
--R
--R                              1
--R   (120)  ----------------------------------------
--R           2   - d x - c 2          - d x - c    2
--R          b (%e         )  + 2a b %e          + a
--R                                                    Type: Expression(Integer)
--E 121
--S 122 of 578
r0024:= -1/a/d/(a+b*exp(1)^(-c-d*x))+log(b+a*exp(1)^(c+d*x))/a^2/d
--R
--R
--R               - d x - c             d x + c
--R          (b %e          + a)log(a %e        + b) - a
--R   (121)  -------------------------------------------
--R                     2      - d x - c    3
--R                    a b d %e          + a d
--R                                                    Type: Expression(Integer)
--E 122
--S 123 of 578
a0024:= integrate(t0024,x)
--R
--R
--R   (122)
--R        - d x - c             - d x - c                - d x - c
--R   (b %e          + a)log(b %e          + a) + b d x %e          + a d x - a

--R   -------------------------------------------------------------------------
--R                             2      - d x - c    3
--R                            a b d %e          + a d
--R                                         Type: Union(Expression(Integer),...)
--E 123
--S 124 of 578
m0024:= a0024-r0024
--R
--R
--R                    d x + c                - d x - c
--R          - log(a %e        + b) + log(b %e          + a) + d x
--R   (123)  -----------------------------------------------------
--R                                    2
--R                                   a d
--R                                                    Type: Expression(Integer)
--E 124
--S 125 of 578
d0024:= D(m0024,x)
--R
--R
--R                              - d x - c  d x + c
--R                        - b %e         %e        + b
--R   (124)  -------------------------------------------------------
--R            2    - d x - c    3   d x + c      2  - d x - c    2
--R          (a b %e          + a )%e        + a b %e          + a b
--R                                                    Type: Expression(Integer)
--E 125
--S 126 of 578
t0025:= 1/(a+b*exp(1)^(-c-d*x))^3
--R
--R
--R                                         1
--R   (125)  --------------------------------------------------------------
--R           3   - d x - c 3       2   - d x - c 2     2    - d x - c    3
--R          b (%e         )  + 3a b (%e         )  + 3a b %e          + a
--R                                                    Type: Expression(Integer)
--E 126
--S 127 of 578
r0025:= -1/2/a/d/(a+b*exp(1)^(-c-d*x))^2-1/a^2/d/(a+b*exp(1)^(-c-d*x))+_
        log(b+a*exp(1)^(c+d*x))/a^3/d
--R
--R
--R   (126)
--R          2   - d x - c 2          - d x - c     2         d x + c
--R       (2b (%e         )  + 4a b %e          + 2a )log(a %e        + b)
--R     +

--R                - d x - c     2
--R       - 2a b %e          - 3a
--R  /
--R       3 2     - d x - c 2     4      - d x - c     5
--R     2a b d (%e         )  + 4a b d %e          + 2a d
--R                                                    Type: Expression(Integer)
--E 127
--S 128 of 578
a0025:= integrate(t0025,x)
--R
--R
--R   (127)
--R          2   - d x - c 2          - d x - c     2         - d x - c
--R       (2b (%e         )  + 4a b %e          + 2a )log(b %e          + a)
--R     +
--R         2       - d x - c 2                      - d x - c     2        2
--R       2b d x (%e         )  + (4a b d x - 2a b)%e          + 2a d x - 3a
--R  /
--R       3 2     - d x - c 2     4      - d x - c     5
--R     2a b d (%e         )  + 4a b d %e          + 2a d
--R                                         Type: Union(Expression(Integer),...)
--E 128
--S 129 of 578
m0025:= a0025-r0025
--R
--R
--R                    d x + c                - d x - c
--R          - log(a %e        + b) + log(b %e          + a) + d x
--R   (128)  -----------------------------------------------------
--R                                    3
--R                                   a d
--R                                                    Type: Expression(Integer)
--E 129
--S 130 of 578
d0025:= D(m0025,x)
--R
--R
--R                              - d x - c  d x + c
--R                        - b %e         %e        + b
--R   (129)  -------------------------------------------------------
--R            3    - d x - c    4   d x + c    2 2  - d x - c    3
--R          (a b %e          + a )%e        + a b %e          + a b
--R                                                    Type: Expression(Integer)
--E 130
--S 131 of 578
t0026:= x/(a+b*exp(1)^(c+d*x))

--R
--R
--R                 x
--R   (130)  ---------------
--R              d x + c
--R          b %e        + a
--R                                                    Type: Expression(Integer)
--E 131
--S 132 of 578
r0026:= -1/2*(-d^2*x^2+2*x*log((a+b*exp(c+d*x))/a)*d+2*_
        polylog(2,-b*exp(c+d*x)/a))/a/d^2
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 132
--S 133 of 578
a0026:= integrate(t0026,x)
--R
--R
--R             x
--R           ++         %A
--R   (131)   |   ---------------- d%A
--R          ++       %A d + c
--R               b %e         + a
--R                                         Type: Union(Expression(Integer),...)
--E 133
--S 134 of 578
m0026:= a0026-r0026
--R
--R
--R             x
--R           ++         %A
--R   (132)   |   ---------------- d%A  - r0026
--R          ++       %A d + c
--R               b %e         + a
--R                                                    Type: Expression(Integer)

--E 134
--S 135 of 578
d0026:= D(m0026,x)
--R
--R
--R                 x
--R   (133)  ---------------
--R              d x + c
--R          b %e        + a
--R                                                    Type: Expression(Integer)
--E 135
--S 136 of 578
t0027:= x^2/(a+b*exp(1)^(c+d*x))
--R
--R
--R                  2
--R                 x
--R   (134)  ---------------
--R              d x + c
--R          b %e        + a
--R                                                    Type: Expression(Integer)
--E 136
--S 137 of 578
r0027:= 1/3*(d^3*x^3-3*x^2*log((a+b*exp(c+d*x))/a)*d^2-6*x*_
        polylog(2,-b*exp(c+d*x)/a)*d+6*_
        polylog(3,-b*exp(c+d*x)/a))/a/d^3
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 137
--S 138 of 578
a0027:= integrate(t0027,x)
--R
--R
--R             x          2

--R           ++         %A
--R   (135)   |   ---------------- d%A
--R          ++       %A d + c
--R               b %e         + a
--R                                         Type: Union(Expression(Integer),...)
--E 138
--S 139 of 578
m0027:= a0027-r0027
--R
--R
--R             x          2
--R           ++         %A
--R   (136)   |   ---------------- d%A  - r0027
--R          ++       %A d + c
--R               b %e         + a
--R                                                    Type: Expression(Integer)
--E 139
--S 140 of 578
d0027:= D(m0027,x)
--R
--R
--R                  2
--R                 x
--R   (137)  ---------------
--R              d x + c
--R          b %e        + a
--R                                                    Type: Expression(Integer)
--E 140
--S 141 of 578
t0028:= x^3/(a+b*exp(1)^(c+d*x))
--R
--R
--R                  3
--R                 x
--R   (138)  ---------------
--R              d x + c
--R          b %e        + a
--R                                                    Type: Expression(Integer)
--E 141
--S 142 of 578
r0028:= 1/4*(x^4*d^4-4*x^3*log((a+b*exp(c+d*x))/a)*d^3-12*x^2*_
        polylog(2,-b*exp(c+d*x)/a)*d^2+24*x*_
        polylog(3,-b*exp(c+d*x)/a)*d-24*_
        polylog(4,-b*exp(c+d*x)/a))/a/d^4
--R
--R   There are no library operations named polylog

--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 142
--S 143 of 578
a0028:= integrate(t0028,x)
--R
--R
--R             x          3
--R           ++         %A
--R   (139)   |   ---------------- d%A
--R          ++       %A d + c
--R               b %e         + a
--R                                         Type: Union(Expression(Integer),...)
--E 143
--S 144 of 578
m0028:= a0028-r0028
--R
--R
--R             x          3
--R           ++         %A
--R   (140)   |   ---------------- d%A  - r0028
--R          ++       %A d + c
--R               b %e         + a
--R                                                    Type: Expression(Integer)
--E 144
--S 145 of 578
d0028:= D(m0028,x)
--R
--R
--R                  3
--R                 x
--R   (141)  ---------------
--R              d x + c
--R          b %e        + a
--R                                                    Type: Expression(Integer)
--E 145

--S 146 of 578
t0029:= x/(a+b*exp(1)^(c+d*x))^2
--R
--R
--R                            x
--R   (142)  ------------------------------------
--R           2   d x + c 2          d x + c    2
--R          b (%e       )  + 2a b %e        + a
--R                                                    Type: Expression(Integer)
--E 146
--S 147 of 578
r0029:= -x/a^2/d+x/a/d/(a+b*exp(1)^(c+d*x))+1/2*x^2/a^2+_
        log(a+b*exp(1)^(c+d*x))/a^2/d^2-_
        x*log(1+b*exp(1)^(c+d*x)/a)/a^2/d-_
        polylog(2,-b*exp(1)^(c+d*x)/a)/a^2/d^2
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 147
--S 148 of 578
a0029:= integrate(t0029,x)
--R
--R
--R             x
--R           ++                    %A
--R   (143)   |   -------------------------------------- d%A
--R          ++    2   %A d + c 2          %A d + c    2
--R               b (%e        )  + 2a b %e         + a
--R                                         Type: Union(Expression(Integer),...)
--E 148
--S 149 of 578
m0029:= a0029-r0029
--R
--R
--R             x
--R           ++                    %A

--R   (144)   |   -------------------------------------- d%A  - r0029
--R          ++    2   %A d + c 2          %A d + c    2
--R               b (%e        )  + 2a b %e         + a
--R                                                    Type: Expression(Integer)
--E 149
--S 150 of 578
d0029:= D(m0029,x)
--R
--R
--R                            x
--R   (145)  ------------------------------------
--R           2   d x + c 2          d x + c    2
--R          b (%e       )  + 2a b %e        + a
--R                                                    Type: Expression(Integer)
--E 150
--S 151 of 578
t0030:= x^2/(a+b*exp(1)^(c+d*x))^2
--R
--R
--R                            2
--R                           x
--R   (146)  ------------------------------------
--R           2   d x + c 2          d x + c    2
--R          b (%e       )  + 2a b %e        + a
--R                                                    Type: Expression(Integer)
--E 151
--S 152 of 578
r0030:= -x^2/a^2/d+x^2/a/d/(a+b*exp(1)^(c+d*x))+_
        1/3*x^3/a^2+2*x*log(1+b*exp(1)^(c+d*x)/a)/a^2/d^2-_
        x^2*log(1+b*exp(1)^(c+d*x)/a)/a^2/d+_
        2*(1-d*x)*polylog(2,-b*exp(1)^(c+d*x)/a)/a^2/d^3+_
        2*polylog(3,-b*exp(1)^(c+d*x)/a)/a^2/d^3
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 152

--S 153 of 578
a0030:= integrate(t0030,x)
--R
--R
--R             x                     2
--R           ++                    %A
--R   (147)   |   -------------------------------------- d%A
--R          ++    2   %A d + c 2          %A d + c    2
--R               b (%e        )  + 2a b %e         + a
--R                                         Type: Union(Expression(Integer),...)
--E 153
--S 154 of 578
m0030:= a0030-r0030
--R
--R
--R             x                     2
--R           ++                    %A
--R   (148)   |   -------------------------------------- d%A  - r0030
--R          ++    2   %A d + c 2          %A d + c    2
--R               b (%e        )  + 2a b %e         + a
--R                                                    Type: Expression(Integer)
--E 154
--S 155 of 578
d0030:= D(m0030,x)
--R
--R
--R                            2
--R                           x
--R   (149)  ------------------------------------
--R           2   d x + c 2          d x + c    2
--R          b (%e       )  + 2a b %e        + a
--R                                                    Type: Expression(Integer)
--E 155
--S 156 of 578
t0031:= x^3/(a+b*exp(1)^(c+d*x))^2
--R
--R
--R                            3
--R                           x
--R   (150)  ------------------------------------
--R           2   d x + c 2          d x + c    2
--R          b (%e       )  + 2a b %e        + a
--R                                                    Type: Expression(Integer)
--E 156
--S 157 of 578

r0031:= -x^3/a^2/d+x^3/a/d/(a+b*exp(1)^(c+d*x))+1/4*x^4/a^2+_
        3*x^2*log(1+b*exp(1)^(c+d*x)/a)/a^2/d^2-_
        x^3*log(1+b*exp(1)^(c+d*x)/a)/a^2/d+3*x*(2-d*x)*_
        polylog(2,-b*exp(1)^(c+d*x)/a)/a^2/d^3-6*(1-d*x)*_
        polylog(3,-b*exp(1)^(c+d*x)/a)/a^2/d^4-6*_
        polylog(4,-b*exp(1)^(c+d*x)/a)/a^2/d^4
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 157
--S 158 of 578
a0031:= integrate(t0031,x)
--R
--R
--R             x                     3
--R           ++                    %A
--R   (151)   |   -------------------------------------- d%A
--R          ++    2   %A d + c 2          %A d + c    2
--R               b (%e        )  + 2a b %e         + a
--R                                         Type: Union(Expression(Integer),...)
--E 158
--S 159 of 578
m0031:= a0031-r0031
--R
--R
--R             x                     3
--R           ++                    %A
--R   (152)   |   -------------------------------------- d%A  - r0031
--R          ++    2   %A d + c 2          %A d + c    2
--R               b (%e        )  + 2a b %e         + a
--R                                                    Type: Expression(Integer)
--E 159
--S 160 of 578
d0031:= D(m0031,x)
--R
--R

--R                            3
--R                           x
--R   (153)  ------------------------------------
--R           2   d x + c 2          d x + c    2
--R          b (%e       )  + 2a b %e        + a
--R                                                    Type: Expression(Integer)
--E 160
--S 161 of 578
t0032:= x/(a+b*exp(1)^(c+d*x))^3
--R
--R
--R                                      x
--R   (154)  --------------------------------------------------------
--R           3   d x + c 3       2   d x + c 2     2    d x + c    3
--R          b (%e       )  + 3a b (%e       )  + 3a b %e        + a
--R                                                    Type: Expression(Integer)
--E 161
--S 162 of 578
r0032:= -1/2/a^2/d^2/(a+b*exp(1)^(c+d*x))-3/2*x/a^3/d+1/2*x^2/a^3+_
        1/2*x*(2*a/d/(a+b*exp(1)^(c+d*x))+(a^2/(a+b*exp(1)^(c+d*x))^2-_
        2*log(a+b*exp(1)^(c+d*x)))/d)/a^3+3/2*_
        log(a+b*exp(1)^(c+d*x))/a^3/d^2+x*_
        log(a+b*exp(1)^(c+d*x))/a^3/d-x*log(1+b*exp(1)^(c+d*x)/a)/a^3/d-_
        polylog(2,-b*exp(1)^(c+d*x)/a)/a^3/d^2
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 162
--S 163 of 578
a0032:= integrate(t0032,x)
--R
--R
--R   (155)
--R      x
--R    ++                               %A
--R    |   ----------------------------------------------------------- d%A

--R   ++    3   %A d + c 3       2   %A d + c 2     2    %A d + c    3
--R        b (%e        )  + 3a b (%e        )  + 3a b %e         + a
--R                                         Type: Union(Expression(Integer),...)
--E 163
--S 164 of 578
m0032:= a0032-r0032
--R
--R
--R   (156)
--R      x
--R    ++                               %A
--R    |   ----------------------------------------------------------- d%A  - r0032
--R   ++    3   %A d + c 3       2   %A d + c 2     2    %A d + c    3
--R        b (%e        )  + 3a b (%e        )  + 3a b %e         + a
--R                                                    Type: Expression(Integer)
--E 164
--S 165 of 578
d0032:= D(m0032,x)
--R
--R
--R                                      x
--R   (157)  --------------------------------------------------------
--R           3   d x + c 3       2   d x + c 2     2    d x + c    3
--R          b (%e       )  + 3a b (%e       )  + 3a b %e        + a
--R                                                    Type: Expression(Integer)
--E 165
--S 166 of 578
t0033:= x^2/(a+b*exp(1)^(c+d*x))^3
--R
--R
--R                                      2
--R                                     x
--R   (158)  --------------------------------------------------------
--R           3   d x + c 3       2   d x + c 2     2    d x + c    3
--R          b (%e       )  + 3a b (%e       )  + 3a b %e        + a
--R                                                    Type: Expression(Integer)
--E 166
--S 167 of 578
r0033:= x/a^3/d^2-x/a^2/d^2/(a+b*exp(1)^(c+d*x))-3/2*x^2/a^3/d+1/3*x^3/a^3+_
        1/2*x^2*(2*a/d/(a+b*exp(1)^(c+d*x))+(a^2/(a+b*exp(1)^(c+d*x))^2-_
        2*log(a+b*exp(1)^(c+d*x)))/d)/a^3-log(a+b*exp(1)^(c+d*x))/a^3/d^3+_
        x^2*log(a+b*exp(1)^(c+d*x))/a^3/d+3*x*_
        log(1+b*exp(1)^(c+d*x)/a)/a^3/d^2-x^2*log(1+b*exp(1)^(c+d*x)/a)/a^3/d+_
        (3-2*d*x)*polylog(2,-b*exp(1)^(c+d*x)/a)/a^3/d^3+2*_
        polylog(3,-b*exp(1)^(c+d*x)/a)/a^3/d^3
--R

--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 167
--S 168 of 578
a0033:= integrate(t0033,x)
--R
--R
--R   (159)
--R      x                               2
--R    ++                              %A
--R    |   ----------------------------------------------------------- d%A
--R   ++    3   %A d + c 3       2   %A d + c 2     2    %A d + c    3
--R        b (%e        )  + 3a b (%e        )  + 3a b %e         + a
--R                                         Type: Union(Expression(Integer),...)
--E 168
--S 169 of 578
m0033:= a0033-r0033
--R
--R
--R   (160)
--R      x                               2
--R    ++                              %A
--R    |   ----------------------------------------------------------- d%A  - r0033
--R   ++    3   %A d + c 3       2   %A d + c 2     2    %A d + c    3
--R        b (%e        )  + 3a b (%e        )  + 3a b %e         + a
--R                                                    Type: Expression(Integer)
--E 169
--S 170 of 578
d0033:= D(m0033,x)
--R
--R
--R                                      2
--R                                     x
--R   (161)  --------------------------------------------------------
--R           3   d x + c 3       2   d x + c 2     2    d x + c    3
--R          b (%e       )  + 3a b (%e       )  + 3a b %e        + a

--S 171 of 578
t0034:= (exp(1)^(a+b*x))^(1/2)/x
--R
--R
--R           +---------+
--R           |  b x + a
--R          \|%e
--R   (162)  ------------
--R                x
--R                                                    Type: Expression(Integer)
--E 171
--S 172 of 578
r0034:= exp(a+b*x)^(1/2)*Ei(1/2*b*x)*exp(-1/2*b*x)
--R
--R
--R                     b x
--R                   - --- +---------+
--R             b x      2  |  b x + a
--R   (163)  Ei(---)%e     \|%e
--R              2
--R                                                    Type: Expression(Integer)
--E 172
--S 173 of 578
a0034:= integrate(t0034,x)
--R
--R
--R   >> Error detected within library code:
--R   integrate: implementation incomplete (constant residues)
--R
--R   Continuing to read the file...
--R
--E 173
--S 174 of 578
m0034:= a0034-r0034
--R
--R
--R                       b x
--R                     - --- +---------+
--R               b x      2  |  b x + a
--R   (164)  - Ei(---)%e     \|%e         + a0034
--R                2
--R                                                    Type: Expression(Integer)
--E 174

--S 175 of 578
d0034:= D(m0034,x)
--R
--R
--R                b x  b x
--R              - ---  --- +---------+
--R                 2    2  |  b x + a
--R            %e     %e   \|%e
--R   (165)  - ------------------------
--R                        x
--R                                                    Type: Expression(Integer)
--E 175
--S 176 of 578
t0035:= (exp(1)^(a+b*x))^(1/2)/x^2
--R
--R
--R           +---------+
--R           |  b x + a
--R          \|%e
--R   (166)  ------------
--R                2
--R               x
--R                                                    Type: Expression(Integer)
--E 176
--S 177 of 578
r0035:= 1/2*exp(-1/2*a-1/2*b*x)*exp(a+b*x)^(1/2)*(-2*exp(1/2*a+1/2*b*x)+_
        b*exp(1/2*a)*Ei(1/2*b*x)*x)/x
--R
--R
--R                - b x - a  b x + a                - b x - a  a
--R                ---------  -------                ---------  -  +---------+
--R                    2         2             b x       2      2  |  b x + a
--R          (- 2%e         %e        + b x Ei(---)%e         %e )\|%e
--R                                             2
--R   (167)  -----------------------------------------------------------------
--R                                          2x
--R                                                    Type: Expression(Integer)
--E 177
--S 178 of 578
a0035:= integrate(t0035,x)
--R
--R
--R   >> Error detected within library code:
--R   integrate: implementation incomplete (constant residues)
--R
--R   Continuing to read the file...
--R

--E 178
--S 179 of 578
m0035:= a0035-r0035
--R
--R
--R   (168)
--R       - b x - a  b x + a                - b x - a  a
--R       ---------  -------                ---------  -  +---------+
--R           2         2             b x       2      2  |  b x + a
--R   (2%e         %e        - b x Ei(---)%e         %e )\|%e         + 2a0035 x
--R                                    2
--R   --------------------------------------------------------------------------
--R                                       2x
--R                                                    Type: Expression(Integer)
--E 179
--S 180 of 578
d0035:= D(m0035,x)
--R
--R
--R                      - b x - a  b x + a         - b x - a  a  b x
--R                      ---------  -------         ---------  -  ---
--R                          2         2                2      2   2    b x + a
--R          ((b x - 2)%e         %e        - b x %e         %e %e   )%e
--R   (169)  ------------------------------------------------------------------
--R                                        +---------+
--R                                      2 |  b x + a
--R                                    2x \|%e
--R                                                    Type: Expression(Integer)
--E 180
--S 181 of 578
t0036:= (exp(1)^(a+b*x))^(1/2)/x^3
--R
--R
--R           +---------+
--R           |  b x + a
--R          \|%e
--R   (170)  ------------
--R                3
--R               x
--R                                                    Type: Expression(Integer)
--E 181
--S 182 of 578
r0036:= 1/8*exp(-1/2*a-1/2*b*x)*exp(a+b*x)^(1/2)*(-4*exp(1/2*a+1/2*b*x)-_
        2*b*exp(1/2*a+1/2*b*x)*x+b^2*exp(1/2*a)*Ei(1/2*b*x)*x^2)/x^2
--R
--R

--R   (171)
--R                  - b x - a  b x + a                - b x - a  a
--R                  ---------  -------                ---------  -  +---------+
--R                      2         2       2 2   b x       2      2  |  b x + a
--R   ((- 2b x - 4)%e         %e        + b x Ei(---)%e         %e )\|%e
--R                                               2
--R   --------------------------------------------------------------------------
--R                                         2
--R                                       8x
--R                                                    Type: Expression(Integer)
--E 182
--S 183 of 578
a0036:= integrate(t0036,x)
--R
--R
--R   >> Error detected within library code:
--R   integrate: implementation incomplete (constant residues)
--R
--R   Continuing to read the file...
--R
--E 183
--S 184 of 578
m0036:= a0036-r0036
--R
--R
--R   (172)
--R                    - b x - a  b x + a                - b x - a  a
--R                    ---------  -------                ---------  -  +---------+
--R                        2         2       2 2   b x       2      2  |  b x + a
--R       ((2b x + 4)%e         %e        - b x Ei(---)%e         %e )\|%e
--R                                                 2
--R     +
--R               2
--R       8a0036 x
--R  /
--R       2
--R     8x
--R                                                    Type: Expression(Integer)
--E 184
--S 185 of 578
d0036:= D(m0036,x)
--R
--R
--R                       - b x - a  b x + a         - b x - a  a  b x
--R                       ---------  -------         ---------  -  ---
--R             2 2           2         2       2 2      2      2   2    b x + a
--R          ((b x  - 8)%e         %e        - b x %e         %e %e   )%e

--R   (173)  -------------------------------------------------------------------
--R                                        +---------+
--R                                      3 |  b x + a
--R                                    8x \|%e
--R                                                    Type: Expression(Integer)
--E 185
--S 186 of 578
t0037:= f^(a+b*(c+d*x)^3)
--R
--R
--R              3 3         2 2       2         3
--R           b d x  + 3b c d x  + 3b c d x + b c  + a
--R   (174)  f
--R                                                    Type: Expression(Integer)
--E 186
--S 187 of 578
r0037:= -1/3*f^a*(c+d*x)*Gamma(1/3,-b*(c+d*x)^3*log(f))/d/_
        (-b*(c+d*x)^3*log(f))^(1/3)
--R
--R
--R                      a _1       3 3         2 2       2         3
--R          (- d x - c)f | (-,(- b d x  - 3b c d x  - 3b c d x - b c )log(f))
--R                          3
--R   (175)  -----------------------------------------------------------------
--R                    +----------------------------------------------+
--R                   3|      3 3         2 2       2         3
--R                 3d\|(- b d x  - 3b c d x  - 3b c d x - b c )log(f)
--R                                                    Type: Expression(Integer)
--E 187
--S 188 of 578
a0037:= integrate(t0037,x)
--R
--R
--R             x    3   3      2     2          2       3
--R           ++   %A b d  + 3%A b c d  + 3%A b c d + b c  + a
--R   (176)   |   f                                           d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 188
--S 189 of 578
m0037:= a0037-r0037
--R
--R
--R   (177)
--R            +----------------------------------------------+
--R           3|      3 3         2 2       2         3

--R         3d\|(- b d x  - 3b c d x  - 3b c d x - b c )log(f)
--R      *
--R            x    3   3      2     2          2       3
--R          ++   %A b d  + 3%A b c d  + 3%A b c d + b c  + a
--R          |   f                                           d%A
--R         ++
--R     +
--R                 a _1       3 3         2 2       2         3
--R       (d x + c)f | (-,(- b d x  - 3b c d x  - 3b c d x - b c )log(f))
--R                     3
--R  /
--R        +----------------------------------------------+
--R       3|      3 3         2 2       2         3
--R     3d\|(- b d x  - 3b c d x  - 3b c d x - b c )log(f)
--R                                                    Type: Expression(Integer)
--E 189
--S 190 of 578
d0037:= D(m0037,x)
--R
--R
--R   (178)
--R               3 3         2 2       2         3
--R        a  (b d x  + 3b c d x  + 3b c d x + b c )log(f)
--R     - f %e
--R   +
--R         3 3         2 2       2         3
--R      b d x  + 3b c d x  + 3b c d x + b c  + a
--R     f
--R                                                    Type: Expression(Integer)
--E 190
--S 191 of 578
t0038:= f^(a+b*(c+d*x)^n)
--R
--R
--R                      n
--R           b (d x + c)  + a
--R   (179)  f
--R                                                    Type: Expression(Integer)
--E 191
--S 192 of 578
r0038:= -f^a*(c+d*x)*Gamma(1/n,-b*(c+d*x)^n*log(f))/_
        ((-b*(c+d*x)^n*log(f))^(1/n))/d/n
--R
--R
--R                      a _1                    n
--R          (- d x - c)f | (-,- b log(f)(d x + c) )
--R                          n

--R   (180)  ---------------------------------------
--R                                          1
--R                                          -
--R                                        n n
--R                d n (- b log(f)(d x + c) )
--R                                                    Type: Expression(Integer)
--E 192
--S 193 of 578
a0038:= integrate(t0038,x)
--R
--R
--R             x              n
--R           ++   b (%A d + c)  + a
--R   (181)   |   f                 d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 193
--S 194 of 578
m0038:= a0038-r0038
--R
--R
--R   (182)
--R                                 1
--R                                 -   x              n
--R                               n n ++   b (%A d + c)  + a
--R       d n (- b log(f)(d x + c) )  |   f                 d%A
--R                                  ++
--R     +
--R                 a _1                    n
--R       (d x + c)f | (-,- b log(f)(d x + c) )
--R                     n
--R  /
--R                               1
--R                               -
--R                             n n
--R     d n (- b log(f)(d x + c) )
--R                                                    Type: Expression(Integer)
--E 194
--S 195 of 578
d0038:= D(m0038,x)
--R
--R
--R   (183)
--R                                   1
--R                                   -
--R            a                    n n
--R           f (- b log(f)(d x + c) )

--R         +
--R                                                                    - n + 1
--R                                                                    -------
--R                               a         n - 1                    n    n
--R           (b d x + b c)log(f)f (d x + c)     (- b log(f)(d x + c) )
--R      *
--R          _1                    n
--R         | (-,- b log(f)(d x + c) )
--R            n
--R     +
--R                                1 2
--R                                -              n
--R                              n n   b (d x + c)  + a
--R       n ((- b log(f)(d x + c) ) ) f
--R     +
--R                                                                   n
--R                                 a         n - 1  b log(f)(d x + c)
--R         (b d n x + b c n)log(f)f (d x + c)     %e
--R      *
--R                               - n + 1                      1
--R                               -------                      -
--R                             n    n                       n n
--R         (- b log(f)(d x + c) )       (- b log(f)(d x + c) )
--R  /
--R                              1 2
--R                              -
--R                            n n
--R     n ((- b log(f)(d x + c) ) )
--R                                                    Type: Expression(Integer)
--E 195
--S 196 of 578
t0039:= f^(a+b*(c+d*x)^(1/2))
--R
--R
--R             +-------+
--R           b\|d x + c  + a
--R   (184)  f
--R                                                    Type: Expression(Integer)
--E 196
--S 197 of 578
r0039:= 2*f^(a+b*(c+d*x)^(1/2))*(-1+(c+d*x)^(1/2)*b*log(f))/b^2/d/log(f)^2
--R
--R
--R                                      +-------+
--R                     +-------+      b\|d x + c  + a
--R          (2b log(f)\|d x + c  - 2)f
--R   (185)  -----------------------------------------
--R                          2        2

--R                         b d log(f)
--R                                                    Type: Expression(Integer)
--E 197
--S 198 of 578
a0039:= integrate(t0039,x)
--R
--R
--R                                              +-------+
--R                     +-------+       b log(f)\|d x + c  + a log(f)
--R          (2b log(f)\|d x + c  - 2)%e
--R   (186)  --------------------------------------------------------
--R                                  2        2
--R                                 b d log(f)
--R                                         Type: Union(Expression(Integer),...)
--E 198
--S 199 of 578
m0039:= a0039-r0039
--R
--R
--R   (187)
--R                                     +-------+
--R                    +-------+      b\|d x + c  + a
--R       (- 2b log(f)\|d x + c  + 2)f
--R     +
--R                                           +-------+
--R                  +-------+       b log(f)\|d x + c  + a log(f)
--R       (2b log(f)\|d x + c  - 2)%e
--R  /
--R      2        2
--R     b d log(f)
--R                                                    Type: Expression(Integer)
--E 199
--S 200 of 578
d0039:= D(m0039,x)
--R
--R
--R               +-------+                  +-------+
--R             b\|d x + c  + a     b log(f)\|d x + c  + a log(f)
--R   (188)  - f                + %e
--R                                                    Type: Expression(Integer)
--E 200
--S 201 of 578
t0040:= f^(a+b*(c+d*x)^(1/3))
--R
--R
--R            3+-------+

--R           b\|d x + c  + a
--R   (189)  f
--R                                                    Type: Expression(Integer)
--E 201
--S 202 of 578
r0040:= 3*f^(a+b*(c+d*x)^(1/3))*(2-2*(c+d*x)^(1/3)*b*log(f)+_
        (c+d*x)^(2/3)*b^2*log(f)^2)/b^3/d/log(f)^3
--R
--R
--R                                                             3+-------+
--R             2      2 3+-------+2           3+-------+      b\|d x + c  + a
--R          (3b log(f)  \|d x + c  - 6b log(f)\|d x + c  + 6)f
--R   (190)  -----------------------------------------------------------------
--R                                      3        3
--R                                     b d log(f)
--R                                                    Type: Expression(Integer)
--E 202
--S 203 of 578
a0040:= integrate(t0040,x)
--R
--R
--R   (191)
--R          2      2 3+-------+2           3+-------+
--R       (3b log(f)  \|d x + c  - 6b log(f)\|d x + c  + 6)
--R    *
--R                 3+-------+
--R         b log(f)\|d x + c  + a log(f)
--R       %e
--R  /
--R      3        3
--R     b d log(f)
--R                                         Type: Union(Expression(Integer),...)
--E 203
--S 204 of 578
m0040:= a0040-r0040
--R
--R
--R   (192)
--R                                                            3+-------+
--R            2      2 3+-------+2           3+-------+      b\|d x + c  + a
--R       (- 3b log(f)  \|d x + c  + 6b log(f)\|d x + c  - 6)f
--R     +
--R            2      2 3+-------+2           3+-------+
--R         (3b log(f)  \|d x + c  - 6b log(f)\|d x + c  + 6)
--R      *
--R                   3+-------+
--R           b log(f)\|d x + c  + a log(f)

--R         %e
--R  /
--R      3        3
--R     b d log(f)
--R                                                    Type: Expression(Integer)
--E 204
--S 205 of 578
d0040:= D(m0040,x)
--R
--R
--R              3+-------+                 3+-------+
--R             b\|d x + c  + a     b log(f)\|d x + c  + a log(f)
--R   (193)  - f                + %e
--R                                                    Type: Expression(Integer)
--E 205
--S 206 of 578
t0041:= x^3*exp(1)^(a+b*x+c*x^2)
--R
--R
--R                 2
--R           3  c x  + b x + a
--R   (194)  x %e
--R                                                    Type: Expression(Integer)
--E 206
--S 207 of 578
r0041:= 1/8*b^2*exp(1)^(a+b*x+c*x^2)/c^3-1/2*exp(1)^(a+b*x+c*x^2)/c^2-_
        1/4*b*exp(1)^(a+b*x+c*x^2)*x/c^2+1/2*exp(1)^(a+b*x+c*x^2)*x^2/c-_
        1/16*b*(b^2-6*c)*exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*_
        erfi(1/2*(b+2*c*x)/c^(1/2))/c^(7/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 207
--S 208 of 578
a0041:= integrate(t0041,x)
--R

--R
--R             x        2
--R           ++    3  %A c + %A b + a
--R   (195)   |   %A %e               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 208
--S 209 of 578
m0041:= a0041-r0041
--R
--R
--R             x        2
--R           ++    3  %A c + %A b + a
--R   (196)   |   %A %e               d%A  - r0041
--R          ++
--R                                                    Type: Expression(Integer)
--E 209
--S 210 of 578
d0041:= D(m0041,x)
--R
--R
--R                 2
--R           3  c x  + b x + a
--R   (197)  x %e
--R                                                    Type: Expression(Integer)
--E 210
--S 211 of 578
t0042:= x^2*exp(1)^(a+b*x+c*x^2)
--R
--R
--R                 2
--R           2  c x  + b x + a
--R   (198)  x %e
--R                                                    Type: Expression(Integer)
--E 211
--S 212 of 578
r0042:= -1/4*b*exp(1)^(a+b*x+c*x^2)/c^2+1/2*exp(1)^(a+b*x+c*x^2)*x/c+_
        1/8*(b^2-2*c)*exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*_
        erfi(1/2*(b+2*c*x)/c^(1/2))/c^(5/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R

--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 212
--S 213 of 578
a0042:= integrate(t0042,x)
--R
--R
--R             x        2
--R           ++    2  %A c + %A b + a
--R   (199)   |   %A %e               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 213
--S 214 of 578
m0042:= a0042-r0042
--R
--R
--R             x        2
--R           ++    2  %A c + %A b + a
--R   (200)   |   %A %e               d%A  - r0042
--R          ++
--R                                                    Type: Expression(Integer)
--E 214
--S 215 of 578
d0042:= D(m0042,x)
--R
--R
--R                 2
--R           2  c x  + b x + a
--R   (201)  x %e
--R                                                    Type: Expression(Integer)
--E 215
--S 216 of 578
t0043:= x^3*exp(1)^((a+b*x)*(c+d*x))
--R
--R
--R                   2
--R           3  b d x  + (a d + b c)x + a c
--R   (202)  x %e
--R                                                    Type: Expression(Integer)
--E 216

--S 217 of 578
r0043:= -1/2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)/b^2/d^2+_
        1/8*(b*c+a*d)^2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)/b^3/d^3-_
        1/4*(b*c+a*d)*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)*x/b^2/d^2+_
        1/2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)*x^2/b/d-_
        1/16*(b^3*c^3-3*b^2*c*(2-a*c)*d-3*a*b*(2-a*c)*d^2+_
        a^3*d^3)*%pi^(1/2)*erfi(1/2*(b*c+a*d+2*b*x*d)/b^(1/2)/d^(1/2))/_
        (exp(1)^(1/4*(b*c-a*d)^2/b/d))/b^(7/2)/d^(7/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 217
--S 218 of 578
a0043:= integrate(t0043,x)
--R
--R
--R             x         2
--R           ++    3  (%A b + %A a)d + (%A b + a)c
--R   (203)   |   %A %e                            d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 218
--S 219 of 578
m0043:= a0043-r0043
--R
--R
--R             x         2
--R           ++    3  (%A b + %A a)d + (%A b + a)c
--R   (204)   |   %A %e                            d%A  - r0043
--R          ++
--R                                                    Type: Expression(Integer)
--E 219
--S 220 of 578
d0043:= D(m0043,x)
--R
--R
--R                   2

--R           3  b d x  + (a d + b c)x + a c
--R   (205)  x %e
--R                                                    Type: Expression(Integer)
--E 220
--S 221 of 578
t0044:= x^2*exp(1)^((a+b*x)*(c+d*x))
--R
--R
--R                   2
--R           2  b d x  + (a d + b c)x + a c
--R   (206)  x %e
--R                                                    Type: Expression(Integer)
--E 221
--S 222 of 578
r0044:= -1/4*(b*c+a*d)*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)/b^2/d^2+_
        1/2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)*x/b/d+_
        1/8*(b^2*c^2-2*b*(1-a*c)*d+a^2*d^2)*%pi^(1/2)*_
        erfi(1/2*(b*c+a*d+2*b*x*d)/b^(1/2)/d^(1/2))/_
        (exp(1)^(1/4*(b*c-a*d)^2/b/d))/b^(5/2)/d^(5/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 222
--S 223 of 578
a0044:= integrate(t0044,x)
--R
--R
--R             x         2
--R           ++    2  (%A b + %A a)d + (%A b + a)c
--R   (207)   |   %A %e                            d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 223
--S 224 of 578
m0044:= a0044-r0044
--R

--R
--R             x         2
--R           ++    2  (%A b + %A a)d + (%A b + a)c
--R   (208)   |   %A %e                            d%A  - r0044
--R          ++
--R                                                    Type: Expression(Integer)
--E 224
--S 225 of 578
d0044:= D(m0044,x)
--R
--R
--R                   2
--R           2  b d x  + (a d + b c)x + a c
--R   (209)  x %e
--R                                                    Type: Expression(Integer)
--E 225
--S 226 of 578
t0045:= x^3*f^(a+b*x+c*x^2)
--R
--R
--R                2
--R           3 c x  + b x + a
--R   (210)  x f
--R                                                    Type: Expression(Integer)
--E 226
--S 227 of 578
r0045:= -1/2*f^(a+b*x+c*x^2)/c^2/log(f)^2+1/8*b^2*f^(a+b*x+c*x^2)/c^3/log(f)-_
        1/4*b*f^(a+b*x+c*x^2)*x/c^2/log(f)+1/2*f^(a+b*x+c*x^2)*x^2/c/log(f)+_
        1/16*b*f^(a-1/4*b^2/c)*%pi^(1/2)*_
        erfi(1/2*(b+2*c*x)*log(f)^(1/2)/c^(1/2))*_
        (6*c-b^2*log(f))/c^(7/2)/log(f)^(3/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 227
--S 228 of 578

a0045:= integrate(t0045,x)
--R
--R
--R             x       2
--R           ++    3 %A c + %A b + a
--R   (211)   |   %A f               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 228
--S 229 of 578
m0045:= a0045-r0045
--R
--R
--R             x       2
--R           ++    3 %A c + %A b + a
--R   (212)   |   %A f               d%A  - r0045
--R          ++
--R                                                    Type: Expression(Integer)
--E 229
--S 230 of 578
d0045:= D(m0045,x)
--R
--R
--R                2
--R           3 c x  + b x + a
--R   (213)  x f
--R                                                    Type: Expression(Integer)
--E 230
--S 231 of 578
t0046:= x^2*f^(a+b*x+c*x^2)
--R
--R
--R                2
--R           2 c x  + b x + a
--R   (214)  x f
--R                                                    Type: Expression(Integer)
--E 231
--S 232 of 578
r0046:= -1/4*b*f^(a+b*x+c*x^2)/c^2/log(f)+1/2*f^(a+b*x+c*x^2)*x/c/log(f)-_
        1/8*f^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)*_
        log(f)^(1/2)/c^(1/2))*(2*c-b^2*log(f))/c^(5/2)/log(f)^(3/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its

--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 232
--S 233 of 578
a0046:= integrate(t0046,x)
--R
--R
--R             x       2
--R           ++    2 %A c + %A b + a
--R   (215)   |   %A f               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 233
--S 234 of 578
m0046:= a0046-r0046
--R
--R
--R             x       2
--R           ++    2 %A c + %A b + a
--R   (216)   |   %A f               d%A  - r0046
--R          ++
--R                                                    Type: Expression(Integer)
--E 234
--S 235 of 578
d0046:= D(m0046,x)
--R
--R
--R                2
--R           2 c x  + b x + a
--R   (217)  x f
--R                                                    Type: Expression(Integer)
--E 235
--S 236 of 578
t0047:= (d+e*x)^3*f^(a+b*x+c*x^2)
--R
--R
--R                                            2
--R            3 3       2 2     2       3  c x  + b x + a
--R   (218)  (e x  + 3d e x  + 3d e x + d )f
--R                                                    Type: Expression(Integer)

--E 236
--S 237 of 578
r0047:= -1/2*e^3*f^(a+b*x+c*x^2)/c^2/log(f)^2+_
        1/8*e*(2*c*d-b*e)^2*f^(a+b*x+c*x^2)/c^3/log(f)+_
        1/4*e*(2*c*d-b*e)*f^(a+b*x+c*x^2)*(d+e*x)/c^2/log(f)+_
        1/2*e*f^(a+b*x+c*x^2)*(d+e*x)^2/c/log(f)-_
        1/16*(2*c*d-b*e)*f^(a-1/4*b^2/c)*%pi^(1/2)*_
        erfi(1/2*(b+2*c*x)*log(f)^(1/2)/c^(1/2))*_
        (6*c*e^2-(2*c*d-b*e)^2*log(f))/c^(7/2)/log(f)^(3/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 237
--S 238 of 578
a0047:= integrate(t0047,x)
--R
--R
--R             x                                     2
--R           ++     3 3      2   2        2     3  %A c + %A b + a
--R   (219)   |   (%A e  + 3%A d e  + 3%A d e + d )f               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 238
--S 239 of 578
m0047:= a0047-r0047
--R
--R
--R             x                                     2
--R           ++     3 3      2   2        2     3  %A c + %A b + a
--R   (220)   |   (%A e  + 3%A d e  + 3%A d e + d )f               d%A  - r0047
--R          ++
--R                                                    Type: Expression(Integer)
--E 239
--S 240 of 578
d0047:= D(m0047,x)
--R

--R
--R                                            2
--R            3 3       2 2     2       3  c x  + b x + a
--R   (221)  (e x  + 3d e x  + 3d e x + d )f
--R                                                    Type: Expression(Integer)
--E 240
--S 241 of 578
t0048:= (d+e*x)^2*f^(a+b*x+c*x^2)
--R
--R
--R                                  2
--R            2 2             2  c x  + b x + a
--R   (222)  (e x  + 2d e x + d )f
--R                                                    Type: Expression(Integer)
--E 241
--S 242 of 578
r0048:= 1/4*e*(4*c*d-b*e)*f^(a+b*x+c*x^2)/c^2/log(f)+_
        1/2*e^2*f^(a+b*x+c*x^2)*x/c/log(f)-_
        1/8*f^(a-1/4*b^2/c)*%pi^(1/2)*_
        erfi(1/2*(b+2*c*x)*log(f)^(1/2)/c^(1/2))*_
        (2*c*e^2-(2*c*d-b*e)^2*log(f))/c^(5/2)/log(f)^(3/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 242
--S 243 of 578
a0048:= integrate(t0048,x)
--R
--R
--R             x                          2
--R           ++     2 2              2  %A c + %A b + a
--R   (223)   |   (%A e  + 2%A d e + d )f               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 243
--S 244 of 578

m0048:= a0048-r0048
--R
--R
--R             x                          2
--R           ++     2 2              2  %A c + %A b + a
--R   (224)   |   (%A e  + 2%A d e + d )f               d%A  - r0048
--R          ++
--R                                                    Type: Expression(Integer)
--E 244
--S 245 of 578
d0048:= D(m0048,x)
--R
--R
--R                                  2
--R            2 2             2  c x  + b x + a
--R   (225)  (e x  + 2d e x + d )f
--R                                                    Type: Expression(Integer)
--E 245
--S 246 of 578
t0049:= (d+e*x)*f^(a+b*x+c*x^2)
--R
--R
--R                       2
--R                    c x  + b x + a
--R   (226)  (e x + d)f
--R                                                    Type: Expression(Integer)
--E 246
--S 247 of 578
r0049:= 1/2*e*f^(a+b*x+c*x^2)/c/log(f)+1/4*(2*c*d-b*e)*_
        f^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)*_
        log(f)^(1/2)/c^(1/2))/c^(3/2)/log(f)^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 247
--S 248 of 578

a0049:= integrate(t0049,x)
--R
--R
--R             x              2
--R           ++             %A c + %A b + a
--R   (227)   |   (%A e + d)f               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 248
--S 249 of 578
m0049:= a0049-r0049
--R
--R
--R             x              2
--R           ++             %A c + %A b + a
--R   (228)   |   (%A e + d)f               d%A  - r0049
--R          ++
--R                                                    Type: Expression(Integer)
--E 249
--S 250 of 578
d0049:= D(m0049,x)
--R
--R
--R                       2
--R                    c x  + b x + a
--R   (229)  (e x + d)f
--R                                                    Type: Expression(Integer)
--E 250
--S 251 of 578
t0050:= (b+2*c*x)^2*f^(a+b*x+c*x^2)
--R
--R
--R                                   2
--R             2 2             2  c x  + b x + a
--R   (230)  (4c x  + 4b c x + b )f
--R                                                    Type: Expression(Integer)
--E 251
--S 252 of 578
r0050:= -c^(1/2)*f^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)*_
        log(f)^(1/2)/c^(1/2))/log(f)^(3/2)+f^(a+b*x+c*x^2)*(b+2*c*x)/log(f)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.

--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 252
--S 253 of 578
a0050:= integrate(t0050,x)
--R
--R
--R             x                           2
--R           ++      2 2              2  %A c + %A b + a
--R   (231)   |   (4%A c  + 4%A b c + b )f               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 253
--S 254 of 578
m0050:= a0050-r0050
--R
--R
--R             x                           2
--R           ++      2 2              2  %A c + %A b + a
--R   (232)   |   (4%A c  + 4%A b c + b )f               d%A  - r0050
--R          ++
--R                                                    Type: Expression(Integer)
--E 254
--S 255 of 578
d0050:= D(m0050,x)
--R
--R
--R                                   2
--R             2 2             2  c x  + b x + a
--R   (233)  (4c x  + 4b c x + b )f
--R                                                    Type: Expression(Integer)
--E 255
--S 256 of 578
t0051:= f^(a+b*x^n)*g^(c+d*x^n)
--R
--R
--R              n        n
--R           b x  + a d x  + c
--R   (234)  f        g
--R                                                    Type: Expression(Integer)
--E 256

--S 257 of 578
r0051:= -f^a*g^c*x*Gamma(1/n,-x^n*(b*log(f)+d*log(g)))/_
        ((-x^n*(b*log(f)+d*log(g)))^(1/n))/n
--R
--R
--R               a c _1                         n
--R            x f g | (-,(- d log(g) - b log(f))x )
--R                     n
--R   (235)  - -------------------------------------
--R                                             1
--R                                             -
--R                                           n n
--R                n ((- d log(g) - b log(f))x )
--R                                                    Type: Expression(Integer)
--E 257
--S 258 of 578
a0051:= integrate(t0051,x)
--R
--R
--R             x      n         n
--R           ++   b %A  + a d %A  + c
--R   (236)   |   f         g         d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 258
--S 259 of 578
m0051:= a0051-r0051
--R
--R
--R   (237)
--R                                    1
--R                                    -   x      n         n
--R                                  n n ++   b %A  + a d %A  + c
--R       n ((- d log(g) - b log(f))x )  |   f         g         d%A
--R                                     ++
--R     +
--R          a c _1                         n
--R       x f g | (-,(- d log(g) - b log(f))x )
--R                n
--R  /
--R                                  1
--R                                  -
--R                                n n
--R     n ((- d log(g) - b log(f))x )
--R                                                    Type: Expression(Integer)
--E 259

--S 260 of 578
d0051:= D(m0051,x)
--R
--R
--R   (238)
--R                                          1
--R                                          -
--R            a c                         n n
--R           f g ((- d log(g) - b log(f))x )
--R         +
--R                                                                       - n + 1
--R                                                                       -------
--R                                   a c n - 1                         n    n
--R         (d x log(g) + b x log(f))f g x     ((- d log(g) - b log(f))x )
--R      *
--R          _1                         n
--R         | (-,(- d log(g) - b log(f))x )
--R            n
--R     +
--R                                     1 2
--R                                     -      n        n
--R                                   n n   b x  + a d x  + c
--R       n (((- d log(g) - b log(f))x ) ) f        g
--R     +
--R                                                                        n
--R                                       a c n - 1  (d log(g) + b log(f))x
--R         (d n x log(g) + b n x log(f))f g x     %e
--R      *
--R                                    - n + 1                           1
--R                                    -------                           -
--R                                  n    n                            n n
--R         ((- d log(g) - b log(f))x )       ((- d log(g) - b log(f))x )
--R  /
--R                                   1 2
--R                                   -
--R                                 n n
--R     n (((- d log(g) - b log(f))x ) )
--R                                                    Type: Expression(Integer)
--E 260
--S 261 of 578
t0052:= exp(1)^(4*x)/(a+b*exp(1)^(2*x))^(2/3)
--R
--R
--R                 4x
--R               %e
--R   (239)  --------------
--R           +----------+2
--R          3|    2x
--R          \|b %e   + a

--S 262 of 578
r0052:= 3/8*(a+b*exp(2*x))^(1/3)*(-3*a+b*exp(2*x))/b^2
--R
--R
--R                         +----------+
--R                2x      3|    2x
--R          (3b %e   - 9a)\|b %e   + a
--R   (240)  ---------------------------
--R                        2
--R                      8b
--R                                                    Type: Expression(Integer)
--E 262
--S 263 of 578
a0052:= integrate(t0052,x)
--R
--R
--R                         +----------+
--R                2x      3|    2x
--R          (3b %e   - 9a)\|b %e   + a
--R   (241)  ---------------------------
--R                        2
--R                      8b
--R                                         Type: Union(Expression(Integer),...)
--E 263
--S 264 of 578
m0052:= a0052-r0052
--R
--R
--R   (242)  0
--R                                                    Type: Expression(Integer)
--E 264
--S 265 of 578
d0052:= D(m0052,x)
--R
--R
--R   (243)  0
--R                                                    Type: Expression(Integer)
--E 265
--S 266 of 578
t0053:= f^(a+b*x)/(c+d*f^(e+2*b*x))
--R
--R
--R               b x + a

--R              f
--R   (244)  ---------------
--R             2b x + e
--R          d f         + c
--R                                                    Type: Expression(Integer)
--E 266
--S 267 of 578
r0053:= f^(a-1/2*e)*_
        arctan(d^(1/2)*f^(1/2*e+b*x)/c^(1/2))/b/c^(1/2)/d^(1/2)/log(f)
--R
--R   There are no library operations named arctan
--R      Use HyperDoc Browse or issue
--R                               )what op arctan
--R      to learn if there is any operation containing " arctan " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctan with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 267
--S 268 of 578
a0053:= integrate(t0053,x)
--R
--R
--R   (245)
--R   [
--R       log
--R                     (e - 2a)log(f)   (b x + a)log(f) 2
--R                (d %e              (%e               )  - c)
--R             *
--R                 +----------------------+
--R                 |        (e - 2a)log(f)
--R                \|- c d %e
--R            +
--R                     (e - 2a)log(f)  (b x + a)log(f)
--R              2c d %e              %e
--R         /
--R                (e - 2a)log(f)   (b x + a)log(f) 2
--R            d %e              (%e               )  + c
--R    /
--R                 +----------------------+
--R                 |        (e - 2a)log(f)
--R       2b log(f)\|- c d %e
--R     ,
--R                           +--------------------+

--R           (b x + a)log(f) |      (e - 2a)log(f)
--R         %e               \|c d %e
--R    atan(----------------------------------------)
--R                             c
--R    ----------------------------------------------]
--R                     +--------------------+
--R                     |      (e - 2a)log(f)
--R            b log(f)\|c d %e
--R                                   Type: Union(List(Expression(Integer)),...)
--E 268
--S 269 of 578
m0053a:= a0053.1-r0053
--R
--R
--R   (246)
--R       log
--R                     (e - 2a)log(f)   (b x + a)log(f) 2
--R                (d %e              (%e               )  - c)
--R             *
--R                 +----------------------+
--R                 |        (e - 2a)log(f)
--R                \|- c d %e
--R            +
--R                     (e - 2a)log(f)  (b x + a)log(f)
--R              2c d %e              %e
--R         /
--R                (e - 2a)log(f)   (b x + a)log(f) 2
--R            d %e              (%e               )  + c
--R     +
--R                         +----------------------+
--R                         |        (e - 2a)log(f)
--R       - 2b r0053 log(f)\|- c d %e
--R  /
--R               +----------------------+
--R               |        (e - 2a)log(f)
--R     2b log(f)\|- c d %e
--R                                                    Type: Expression(Integer)
--E 269
--S 270 of 578
d0053a:= D(m0053a,x)
--R
--R
--R                         (b x + a)log(f)
--R                       %e
--R   (247)  ------------------------------------------
--R              (e - 2a)log(f)   (b x + a)log(f) 2
--R          d %e              (%e               )  + c
--R                                                    Type: Expression(Integer)

--E 270
--S 271 of 578
m0053b:= a0053.2-r0053
--R
--R
--R   (248)
--R                              +--------------------+
--R              (b x + a)log(f) |      (e - 2a)log(f)
--R            %e               \|c d %e
--R       atan(----------------------------------------)
--R                                c
--R     +
--R                        +--------------------+
--R                        |      (e - 2a)log(f)
--R       - b r0053 log(f)\|c d %e
--R  /
--R              +--------------------+
--R              |      (e - 2a)log(f)
--R     b log(f)\|c d %e
--R                                                    Type: Expression(Integer)
--E 271
--S 272 of 578
d0053b:= D(m0053b,x)
--R
--R
--R                         (b x + a)log(f)
--R                       %e
--R   (249)  ------------------------------------------
--R              (e - 2a)log(f)   (b x + a)log(f) 2
--R          d %e              (%e               )  + c
--R                                                    Type: Expression(Integer)
--E 272
--S 273 of 578
t0054:= f^(a+2*b*x)/(c+d*f^(e+2*b*x))
--R
--R
--R              2b x + a
--R             f
--R   (250)  ---------------
--R             2b x + e
--R          d f         + c
--R                                                    Type: Expression(Integer)
--E 273
--S 274 of 578
r0054:= 1/2*f^(a-e)*log(c+d*f^(e+2*b*x))/b/d/log(f)
--R

--R
--R           - e + a       2b x + e
--R          f       log(d f         + c)
--R   (251)  ----------------------------
--R                   2b d log(f)
--R                                                    Type: Expression(Integer)
--E 274
--S 275 of 578
a0054:= integrate(t0054,x)
--R
--R
--R            (- e + a)log(f)        (2b x + e)log(f)
--R          %e               log(d %e                 + c)
--R   (252)  ----------------------------------------------
--R                            2b d log(f)
--R                                         Type: Union(Expression(Integer),...)
--E 275
--S 276 of 578
m0054:= a0054-r0054
--R
--R
--R   (253)
--R     (- e + a)log(f)        (2b x + e)log(f)         - e + a       2b x + e
--R   %e               log(d %e                 + c) - f       log(d f         + c)
--R   -----------------------------------------------------------------------------
--R                                    2b d log(f)
--R                                                    Type: Expression(Integer)
--E 276
--S 277 of 578
d0054:= D(m0054,x)
--R
--R
--R   (254)
--R              2b x + e       (- e + a)log(f)      - e + a 2b x + e
--R         ((d f         + c)%e                - d f       f        )
--R      *
--R           (2b x + e)log(f)
--R         %e
--R     +
--R            - e + a 2b x + e
--R       - c f       f
--R  /
--R       2 2b x + e         (2b x + e)log(f)        2b x + e    2
--R     (d f         + c d)%e                 + c d f         + c
--R                                                    Type: Expression(Integer)
--E 277

--S 278 of 578
t0055:= f^(a+3*b*x)/(c+d*f^(e+2*b*x))
--R
--R
--R              3b x + a
--R             f
--R   (255)  ---------------
--R             2b x + e
--R          d f         + c
--R                                                    Type: Expression(Integer)
--E 278
--S 279 of 578
r0055:= -(-f^(a-e+b*x)*d^(1/2)+c^(1/2)*f^(a-2*e)*(f^e)^(1/2)*_
        arctan(d^(1/2)*f^(b*x)*(f^e)^(1/2)/c^(1/2)))/b/d^(3/2)/log(f)
--R
--R   There are no library operations named arctan
--R      Use HyperDoc Browse or issue
--R                               )what op arctan
--R      to learn if there is any operation containing " arctan " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctan with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 279
--S 280 of 578
a0055:= integrate(t0055,x)
--R
--R
--R   (256)
--R   [
--R                   (- 3e + 2a)log(f)
--R            +---+  -----------------
--R            |  c           2
--R            |- - %e
--R           \|  d
--R        *
--R                    (2b x + e)log(f) 2             (2b x + e)log(f)
--R                    ----------------        +---+  ----------------
--R                            2               |  c           2
--R               d (%e                )  - 2d |- - %e                 - c
--R                                           \|  d
--R           log(--------------------------------------------------------)
--R                                   (2b x + e)log(f) 2
--R                                   ----------------

--R                                           2
--R                              d (%e                )  + c
--R       +
--R            (- 3e + 2a)log(f)  (2b x + e)log(f)
--R            -----------------  ----------------
--R                    2                  2
--R         2%e                 %e
--R    /
--R       2b d log(f)
--R     ,
--R
--R                                         (2b x + e)log(f)
--R                 (- 3e + 2a)log(f)       ----------------
--R            +-+  -----------------               2
--R            |c           2             %e
--R         -  |- %e                 atan(------------------)
--R           \|d                                 +-+
--R                                               |c
--R                                               |-
--R                                              \|d
--R       +
--R           (- 3e + 2a)log(f)  (2b x + e)log(f)
--R           -----------------  ----------------
--R                   2                  2
--R         %e                 %e
--R    /
--R       b d log(f)
--R     ]
--R                                   Type: Union(List(Expression(Integer)),...)
--E 280
--S 281 of 578
m0055a:= a0055.1-r0055
--R
--R
--R   (257)
--R                 (- 3e + 2a)log(f)
--R          +---+  -----------------
--R          |  c           2
--R          |- - %e
--R         \|  d
--R      *
--R                  (2b x + e)log(f) 2             (2b x + e)log(f)
--R                  ----------------        +---+  ----------------
--R                          2               |  c           2
--R             d (%e                )  - 2d |- - %e                 - c
--R                                         \|  d
--R         log(--------------------------------------------------------)
--R                                 (2b x + e)log(f) 2
--R                                 ----------------

--R                                         2
--R                            d (%e                )  + c
--R     +
--R          (- 3e + 2a)log(f)  (2b x + e)log(f)
--R          -----------------  ----------------
--R                  2                  2
--R       2%e                 %e                 - 2b d r0055 log(f)
--R  /
--R     2b d log(f)
--R                                                    Type: Expression(Integer)
--E 281
--S 282 of 578
d0055a:= D(m0055a,x)
--R
--R
--R            (- 3e + 2a)log(f)   (2b x + e)log(f) 3
--R            -----------------   ----------------
--R                    2                   2
--R          %e                 (%e                )
--R   (258)  ----------------------------------------
--R                      (2b x + e)log(f) 2
--R                      ----------------
--R                              2
--R                 d (%e                )  + c
--R                                                    Type: Expression(Integer)
--E 282
--S 283 of 578
m0055b:= a0055.2-r0055
--R
--R
--R   (259)
--R                                       (2b x + e)log(f)
--R               (- 3e + 2a)log(f)       ----------------
--R          +-+  -----------------               2
--R          |c           2             %e
--R       -  |- %e                 atan(------------------)
--R         \|d                                 +-+
--R                                             |c
--R                                             |-
--R                                            \|d
--R     +
--R         (- 3e + 2a)log(f)  (2b x + e)log(f)
--R         -----------------  ----------------
--R                 2                  2
--R       %e                 %e                 - b d r0055 log(f)
--R  /
--R     b d log(f)
--R                                                    Type: Expression(Integer)

--E 283
--S 284 of 578
d0055b:= D(m0055b,x)
--R
--R
--R            (- 3e + 2a)log(f)   (2b x + e)log(f) 3
--R            -----------------   ----------------
--R                    2                   2
--R          %e                 (%e                )
--R   (260)  ----------------------------------------
--R                      (2b x + e)log(f) 2
--R                      ----------------
--R                              2
--R                 d (%e                )  + c
--R                                                    Type: Expression(Integer)
--E 284
--S 285 of 578
t0056:= f^(a+5*b*x)/(c+d*f^(e+2*b*x))
--R
--R
--R              5b x + a
--R             f
--R   (261)  ---------------
--R             2b x + e
--R          d f         + c
--R                                                    Type: Expression(Integer)
--E 285
--S 286 of 578
r0056:= -1/3/d^(5/2)*(3*c*f^(a-2*e+b*x)*d^(1/2)-f^(a-e+3*b*x)*d^(3/2)-_
        3*c^(3/2)*f^(a-3*e)*(f^e)^(1/2)*_
        arctan(d^(1/2)*f^(b*x)*(f^e)^(1/2)/c^(1/2)))/b/log(f)
--R
--R   There are no library operations named arctan
--R      Use HyperDoc Browse or issue
--R                               )what op arctan
--R      to learn if there is any operation containing " arctan " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctan with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 286
--S 287 of 578

a0056:= integrate(t0056,x)
--R
--R
--R   (262)
--R   [
--R                     (- 5e + 2a)log(f)
--R              +---+  -----------------
--R              |  c           2
--R           3c |- - %e
--R             \|  d
--R        *
--R                    (2b x + e)log(f) 2             (2b x + e)log(f)
--R                    ----------------        +---+  ----------------
--R                            2               |  c           2
--R               d (%e                )  + 2d |- - %e                 - c
--R                                           \|  d
--R           log(--------------------------------------------------------)
--R                                   (2b x + e)log(f) 2
--R                                   ----------------
--R                                           2
--R                              d (%e                )  + c
--R       +
--R              (- 5e + 2a)log(f)   (2b x + e)log(f) 3
--R              -----------------   ----------------
--R                      2                   2
--R         2d %e                 (%e                )
--R       +
--R                (- 5e + 2a)log(f)  (2b x + e)log(f)
--R                -----------------  ----------------
--R                        2                  2
--R         - 6c %e                 %e
--R    /
--R           2
--R       6b d log(f)
--R     ,
--R
--R                                         (2b x + e)log(f)
--R                 (- 5e + 2a)log(f)       ----------------
--R            +-+  -----------------               2
--R            |c           2             %e
--R         3c |- %e                 atan(------------------)
--R           \|d                                 +-+
--R                                               |c
--R                                               |-
--R                                              \|d
--R       +
--R             (- 5e + 2a)log(f)   (2b x + e)log(f) 3
--R             -----------------   ----------------
--R                     2                   2
--R         d %e                 (%e                )

--R       +
--R                (- 5e + 2a)log(f)  (2b x + e)log(f)
--R                -----------------  ----------------
--R                        2                  2
--R         - 3c %e                 %e
--R    /
--R           2
--R       3b d log(f)
--R     ]
--R                                   Type: Union(List(Expression(Integer)),...)
--E 287
--S 288 of 578
m0056a:= a0056.1-r0056
--R
--R
--R   (263)
--R                   (- 5e + 2a)log(f)
--R            +---+  -----------------
--R            |  c           2
--R         3c |- - %e
--R           \|  d
--R      *
--R                  (2b x + e)log(f) 2             (2b x + e)log(f)
--R                  ----------------        +---+  ----------------
--R                          2               |  c           2
--R             d (%e                )  + 2d |- - %e                 - c
--R                                         \|  d
--R         log(--------------------------------------------------------)
--R                                 (2b x + e)log(f) 2
--R                                 ----------------
--R                                         2
--R                            d (%e                )  + c
--R     +
--R            (- 5e + 2a)log(f)   (2b x + e)log(f) 3
--R            -----------------   ----------------
--R                    2                   2
--R       2d %e                 (%e                )
--R     +
--R              (- 5e + 2a)log(f)  (2b x + e)log(f)
--R              -----------------  ----------------
--R                      2                  2              2
--R       - 6c %e                 %e                 - 6b d r0056 log(f)
--R  /
--R         2
--R     6b d log(f)
--R                                                    Type: Expression(Integer)
--E 288
--S 289 of 578

d0056a:= D(m0056a,x)
--R
--R
--R            (- 5e + 2a)log(f)   (2b x + e)log(f) 5
--R            -----------------   ----------------
--R                    2                   2
--R          %e                 (%e                )
--R   (264)  ----------------------------------------
--R                      (2b x + e)log(f) 2
--R                      ----------------
--R                              2
--R                 d (%e                )  + c
--R                                                    Type: Expression(Integer)
--E 289
--S 290 of 578
m0056b:= a0056.2-r0056
--R
--R
--R   (265)
--R                                       (2b x + e)log(f)
--R               (- 5e + 2a)log(f)       ----------------
--R          +-+  -----------------               2
--R          |c           2             %e
--R       3c |- %e                 atan(------------------)
--R         \|d                                 +-+
--R                                             |c
--R                                             |-
--R                                            \|d
--R     +
--R           (- 5e + 2a)log(f)   (2b x + e)log(f) 3
--R           -----------------   ----------------
--R                   2                   2
--R       d %e                 (%e                )
--R     +
--R              (- 5e + 2a)log(f)  (2b x + e)log(f)
--R              -----------------  ----------------
--R                      2                  2              2
--R       - 3c %e                 %e                 - 3b d r0056 log(f)
--R  /
--R         2
--R     3b d log(f)
--R                                                    Type: Expression(Integer)
--E 290
--S 291 of 578
d0056b:= D(m0056b,x)
--R
--R
--R            (- 5e + 2a)log(f)   (2b x + e)log(f) 5

--R            -----------------   ----------------
--R                    2                   2
--R          %e                 (%e                )
--R   (266)  ----------------------------------------
--R                      (2b x + e)log(f) 2
--R                      ----------------
--R                              2
--R                 d (%e                )  + c
--R                                                    Type: Expression(Integer)
--E 291
--S 292 of 578
t0057:= x*exp(x)/(1+exp(1)^(2*x))
--R
--R
--R                x
--R            x %e
--R   (267)  --------
--R            2x
--R          %e   + 1
--R                                                    Type: Expression(Integer)
--E 292
--S 293 of 578
r0057:= x*arctan(exp(x))-_
        1/2*%i*polylog(2,-%i*exp(x))+_
        1/2*%i*polylog(2,%i*exp(x))
--R
--R   There are no library operations named arctan
--R      Use HyperDoc Browse or issue
--R                               )what op arctan
--R      to learn if there is any operation containing " arctan " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctan with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 293
--S 294 of 578
a0057:= integrate(t0057,x)
--R
--R
--R             x       %A
--R           ++   %A %e
--R   (268)   |   --------- d%A
--R          ++     2%A

--R               %e    + 1
--R                                         Type: Union(Expression(Integer),...)
--E 294
--S 295 of 578
m0057:= a0057-r0057
--R
--R
--R             x       %A
--R           ++   %A %e
--R   (269)   |   --------- d%A  - r0057
--R          ++     2%A
--R               %e    + 1
--R                                                    Type: Expression(Integer)
--E 295
--S 296 of 578
d0057:= D(m0057,x)
--R
--R
--R                x
--R            x %e
--R   (270)  --------
--R            2x
--R          %e   + 1
--R                                                    Type: Expression(Integer)
--E 296
--S 297 of 578
t0058:= x^2*exp(x)/(1+exp(1)^(2*x))
--R
--R
--R             2  x
--R            x %e
--R   (271)  --------
--R            2x
--R          %e   + 1
--R                                                    Type: Expression(Integer)
--E 297
--S 298 of 578
r0058:= x^2*arctan(exp(x))-%i*x*_
        polylog(2,-%i*exp(x))+%i*x*polylog(2,%i*exp(x))+_
        %i*polylog(3,-%i*exp(x))-%i*polylog(3,%i*exp(x))
--R
--R   There are no library operations named arctan
--R      Use HyperDoc Browse or issue
--R                               )what op arctan
--R      to learn if there is any operation containing " arctan " in its
--R      name.

--R
--R   Cannot find a definition or applicable library operation named
--R      arctan with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 298
--S 299 of 578
a0058:= integrate(t0058,x)
--R
--R
--R             x    2  %A
--R           ++   %A %e
--R   (272)   |   --------- d%A
--R          ++     2%A
--R               %e    + 1
--R                                         Type: Union(Expression(Integer),...)
--E 299
--S 300 of 578
m0058:= a0058-r0058
--R
--R
--R             x    2  %A
--R           ++   %A %e
--R   (273)   |   --------- d%A  - r0058
--R          ++     2%A
--R               %e    + 1
--R                                                    Type: Expression(Integer)
--E 300
--S 301 of 578
d0058:= D(m0058,x)
--R
--R
--R             2  x
--R            x %e
--R   (274)  --------
--R            2x
--R          %e   + 1
--R                                                    Type: Expression(Integer)
--E 301
--S 302 of 578
t0059:= x^3*exp(x)/(1+exp(1)^(2*x))
--R
--R
--R             3  x

--R            x %e
--R   (275)  --------
--R            2x
--R          %e   + 1
--R                                                    Type: Expression(Integer)
--E 302
--S 303 of 578
r0059:= x^3*arctan(exp(x))-3/2*%i*x^2*polylog(2,-%i*exp(x))+_
        3/2*%i*x^2*polylog(2,%i*exp(x))+_
        3*%i*x*polylog(3,-%i*exp(x))-_
        3*%i*x*polylog(3,%i*exp(x))-_
        3*%i*polylog(4,-%i*exp(x))+_
        3*%i*polylog(4,%i*exp(x))
--R
--R   There are no library operations named arctan
--R      Use HyperDoc Browse or issue
--R                               )what op arctan
--R      to learn if there is any operation containing " arctan " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctan with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 303
--S 304 of 578
a0059:= integrate(t0059,x)
--R
--R
--R             x    3  %A
--R           ++   %A %e
--R   (276)   |   --------- d%A
--R          ++     2%A
--R               %e    + 1
--R                                         Type: Union(Expression(Integer),...)
--E 304
--S 305 of 578
m0059:= a0059-r0059
--R
--R
--R             x    3  %A
--R           ++   %A %e
--R   (277)   |   --------- d%A  - r0059
--R          ++     2%A
--R               %e    + 1

--S 306 of 578
d0059:= D(m0059,x)
--R
--R
--R             3  x
--R            x %e
--R   (278)  --------
--R            2x
--R          %e   + 1
--R                                                    Type: Expression(Integer)
--E 306
--S 307 of 578
t0060:= x*exp(x)/(1-exp(1)^(2*x))
--R
--R
--R                  x
--R              x %e
--R   (279)  - --------
--R              2x
--R            %e   - 1
--R                                                    Type: Expression(Integer)
--E 307
--S 308 of 578
r0060:= x*arctanh(exp(x))+1/2*polylog(2,-exp(x))-1/2*polylog(2,exp(x))
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 308
--S 309 of 578
a0060:= integrate(t0060,x)
--R
--R
--R             x         %A
--R           ++     %A %e

--R   (280)   |   - --------- d%A
--R          ++       2%A
--R                 %e    - 1
--R                                         Type: Union(Expression(Integer),...)
--E 309
--S 310 of 578
m0060:= a0060-r0060
--R
--R
--R             x         %A
--R           ++     %A %e
--R   (281)   |   - --------- d%A  - r0060
--R          ++       2%A
--R                 %e    - 1
--R                                                    Type: Expression(Integer)
--E 310
--S 311 of 578
d0060:= D(m0060,x)
--R
--R
--R                  x
--R              x %e
--R   (282)  - --------
--R              2x
--R            %e   - 1
--R                                                    Type: Expression(Integer)
--E 311
--S 312 of 578
t0061:= x^2*exp(x)/(1-exp(1)^(2*x))
--R
--R
--R               2  x
--R              x %e
--R   (283)  - --------
--R              2x
--R            %e   - 1
--R                                                    Type: Expression(Integer)
--E 312
--S 313 of 578
r0061:= x^2*arctanh(exp(x))+x*polylog(2,-exp(x))-_
        x*polylog(2,exp(x))-_
        polylog(3,-exp(x))+polylog(3,exp(x))
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh

--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 313
--S 314 of 578
a0061:= integrate(t0061,x)
--R
--R
--R             x      2  %A
--R           ++     %A %e
--R   (284)   |   - --------- d%A
--R          ++       2%A
--R                 %e    - 1
--R                                         Type: Union(Expression(Integer),...)
--E 314
--S 315 of 578
m0061:= a0061-r0061
--R
--R
--R             x      2  %A
--R           ++     %A %e
--R   (285)   |   - --------- d%A  - r0061
--R          ++       2%A
--R                 %e    - 1
--R                                                    Type: Expression(Integer)
--E 315
--S 316 of 578
d0061:= D(m0061,x)
--R
--R
--R               2  x
--R              x %e
--R   (286)  - --------
--R              2x
--R            %e   - 1
--R                                                    Type: Expression(Integer)
--E 316
--S 317 of 578
t0062:= x^3*exp(x)/(1-exp(1)^(2*x))
--R

--R
--R               3  x
--R              x %e
--R   (287)  - --------
--R              2x
--R            %e   - 1
--R                                                    Type: Expression(Integer)
--E 317
--S 318 of 578
r0062:= x^3*arctanh(exp(x))+3/2*x^2*polylog(2,-exp(x))-_
        3/2*x^2*polylog(2,exp(x))-3*x*polylog(3,-exp(x))+_
        3*x*polylog(3,exp(x))+3*polylog(4,-exp(x))-3*polylog(4,exp(x))
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 318
--S 319 of 578
a0062:= integrate(t0062,x)
--R
--R
--R             x      3  %A
--R           ++     %A %e
--R   (288)   |   - --------- d%A
--R          ++       2%A
--R                 %e    - 1
--R                                         Type: Union(Expression(Integer),...)
--E 319
--S 320 of 578
m0062:= a0062-r0062
--R
--R
--R             x      3  %A
--R           ++     %A %e
--R   (289)   |   - --------- d%A  - r0062
--R          ++       2%A
--R                 %e    - 1
--R                                                    Type: Expression(Integer)

--E 320
--S 321 of 578
d0062:= D(m0062,x)
--R
--R
--R               3  x
--R              x %e
--R   (290)  - --------
--R              2x
--R            %e   - 1
--R                                                    Type: Expression(Integer)
--E 321
--S 322 of 578
t0063:= f^x/(a+b*f^(2*x))
--R
--R
--R               x
--R              f
--R   (291)  ---------
--R             2x
--R          b f   + a
--R                                                    Type: Expression(Integer)
--E 322
--S 323 of 578
r0063:= arctan(b^(1/2)*f^x/a^(1/2))/a^(1/2)/b^(1/2)/log(f)
--R
--R   There are no library operations named arctan
--R      Use HyperDoc Browse or issue
--R                               )what op arctan
--R      to learn if there is any operation containing " arctan " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctan with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 323
--S 324 of 578
a0063:= integrate(t0063,x)
--R
--R
--R   (292)
--R          +-----+   x log(f) 2          x log(f)     +-----+
--R        b\|- a b (%e        )  + 2a b %e         - a\|- a b

--R    log(----------------------------------------------------)
--R                              x log(f) 2
--R                         b (%e        )  + a
--R   [---------------------------------------------------------,
--R                                 +-----+
--R                         2log(f)\|- a b
--R          +---+  x log(f)
--R         \|a b %e
--R    atan(----------------)
--R                 a
--R    ----------------------]
--R                +---+
--R         log(f)\|a b
--R                                   Type: Union(List(Expression(Integer)),...)
--E 324
--S 325 of 578
m0063a:= a0063.1-r0063
--R
--R
--R   (293)
--R             +-----+   x log(f) 2          x log(f)     +-----+
--R           b\|- a b (%e        )  + 2a b %e         - a\|- a b
--R       log(----------------------------------------------------)
--R                                 x log(f) 2
--R                            b (%e        )  + a
--R     +
--R                       +-----+
--R       - 2r0063 log(f)\|- a b
--R  /
--R             +-----+
--R     2log(f)\|- a b
--R                                                    Type: Expression(Integer)
--E 325
--S 326 of 578
d0063a:= D(m0063a,x)
--R
--R
--R                 x log(f)
--R               %e
--R   (294)  -------------------
--R               x log(f) 2
--R          b (%e        )  + a
--R                                                    Type: Expression(Integer)
--E 326
--S 327 of 578
m0063b:= a0063.2-r0063
--R

--R
--R                +---+  x log(f)
--R               \|a b %e                         +---+
--R          atan(----------------) - r0063 log(f)\|a b
--R                       a
--R   (295)  -------------------------------------------
--R                                 +---+
--R                          log(f)\|a b
--R                                                    Type: Expression(Integer)
--E 327
--S 328 of 578
d0063b:= D(m0063b,x)
--R
--R
--R                 x log(f)
--R               %e
--R   (296)  -------------------
--R               x log(f) 2
--R          b (%e        )  + a
--R                                                    Type: Expression(Integer)
--E 328
--S 329 of 578
t0064:= x*f^x/(a+b*f^(2*x))
--R
--R
--R                x
--R             x f
--R   (297)  ---------
--R             2x
--R          b f   + a
--R                                                    Type: Expression(Integer)
--E 329
--S 330 of 578
r0064:= 1/2*(2*x*arctan(b^(1/2)*f^x/a^(1/2))*log(f)-_
        %i*polylog(2,-%i*b^(1/2)*f^x/a^(1/2))+_
        %i*polylog(2,%i*b^(1/2)*f^x/a^(1/2)))/a^(1/2)/b^(1/2)/log(f)^2
--R
--R   There are no library operations named arctan
--R      Use HyperDoc Browse or issue
--R                               )what op arctan
--R      to learn if there is any operation containing " arctan " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctan with argument type(s)
--R                             Expression(Integer)
--R

--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 330
--S 331 of 578
a0064:= integrate(t0064,x)
--R
--R
--R             x       %A
--R           ++    %A f
--R   (298)   |   ---------- d%A
--R          ++      2%A
--R               b f    + a
--R                                         Type: Union(Expression(Integer),...)
--E 331
--S 332 of 578
m0064:= a0064-r0064
--R
--R
--R             x       %A
--R           ++    %A f
--R   (299)   |   ---------- d%A  - r0064
--R          ++      2%A
--R               b f    + a
--R                                                    Type: Expression(Integer)
--E 332
--S 333 of 578
d0064:= D(m0064,x)
--R
--R
--R                x
--R             x f
--R   (300)  ---------
--R             2x
--R          b f   + a
--R                                                    Type: Expression(Integer)
--E 333
--S 334 of 578
t0065:= x^2*f^x/(a+b*f^(2*x))
--R
--R
--R              2 x
--R             x f
--R   (301)  ---------
--R             2x
--R          b f   + a
--R                                                    Type: Expression(Integer)

--E 334
--S 335 of 578
r0065:= (x^2*arctan(b^(1/2)*f^x/a^(1/2))*log(f)^2-_
        %i*x*polylog(2,-%i*b^(1/2)*f^x/a^(1/2))*log(f)+_
        %i*x*polylog(2,%i*b^(1/2)*f^x/a^(1/2))*log(f)+_
        %i*polylog(3,-%i*b^(1/2)*f^x/a^(1/2))-_
        %i*polylog(3,%i*b^(1/2)*f^x/a^(1/2)))/a^(1/2)/b^(1/2)/log(f)^3
--R
--R   There are no library operations named arctan
--R      Use HyperDoc Browse or issue
--R                               )what op arctan
--R      to learn if there is any operation containing " arctan " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctan with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 335
--S 336 of 578
a0065:= integrate(t0065,x)
--R
--R
--R             x     2 %A
--R           ++    %A f
--R   (302)   |   ---------- d%A
--R          ++      2%A
--R               b f    + a
--R                                         Type: Union(Expression(Integer),...)
--E 336
--S 337 of 578
m0065:= a0065-r0065
--R
--R
--R             x     2 %A
--R           ++    %A f
--R   (303)   |   ---------- d%A  - r0065
--R          ++      2%A
--R               b f    + a
--R                                                    Type: Expression(Integer)
--E 337
--S 338 of 578
d0065:= D(m0065,x)
--R

--R
--R              2 x
--R             x f
--R   (304)  ---------
--R             2x
--R          b f   + a
--R                                                    Type: Expression(Integer)
--E 338
--S 339 of 578
t0066:= x^3*f^x/(a+b*f^(2*x))
--R
--R
--R              3 x
--R             x f
--R   (305)  ---------
--R             2x
--R          b f   + a
--R                                                    Type: Expression(Integer)
--E 339
--S 340 of 578
r0066:= 1/2*(2*x^3*arctan(b^(1/2)*f^x/a^(1/2))*log(f)^3-_
        3*%i*x^2*polylog(2,-%i*b^(1/2)*f^x/a^(1/2))*log(f)^2+_
        3*%i*x^2*polylog(2,%i*b^(1/2)*f^x/a^(1/2))*log(f)^2+_
        6*%i*x*polylog(3,-%i*b^(1/2)*f^x/a^(1/2))*log(f)-_
        6*%i*x*polylog(3,%i*b^(1/2)*f^x/a^(1/2))*log(f)-_
        6*%i*polylog(4,-%i*b^(1/2)*f^x/a^(1/2))+_
        6*%i*polylog(4,%i*b^(1/2)*f^x/a^(1/2)))/a^(1/2)/b^(1/2)/log(f)^4
--R
--R   There are no library operations named arctan
--R      Use HyperDoc Browse or issue
--R                               )what op arctan
--R      to learn if there is any operation containing " arctan " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctan with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 340
--S 341 of 578
a0066:= integrate(t0066,x)
--R
--R
--R             x     3 %A
--R           ++    %A f

--R   (306)   |   ---------- d%A
--R          ++      2%A
--R               b f    + a
--R                                         Type: Union(Expression(Integer),...)
--E 341
--S 342 of 578
m0066:= a0066-r0066
--R
--R
--R             x     3 %A
--R           ++    %A f
--R   (307)   |   ---------- d%A  - r0066
--R          ++      2%A
--R               b f    + a
--R                                                    Type: Expression(Integer)
--E 342
--S 343 of 578
d0066:= D(m0066,x)
--R
--R
--R              3 x
--R             x f
--R   (308)  ---------
--R             2x
--R          b f   + a
--R                                                    Type: Expression(Integer)
--E 343
--S 344 of 578
t0067:= x/(3+3*exp(x)+exp(1)^(2*x))
--R
--R
--R                 x
--R   (309)  ---------------
--R            2x      x
--R          %e   + 3%e  + 3
--R                                                    Type: Expression(Integer)
--E 344
--S 345 of 578
r0067:= -1/3*%i*x^2*3^(1/2)/(3-%i*3^(1/2))+_
        1/3*%i*x^2*3^(1/2)/(3+%i*3^(1/2))+_
        2/3*%i*x*log(1+2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_
        2/3*%i*x*log(1+2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))+_
        2/3*%i*polylog(2,-2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_
        2/3*%i*polylog(2,-2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))
--R
--R   There are no library operations named polylog

--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                        Expression(Complex(Integer))
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 345
--S 346 of 578
a0067:= integrate(t0067,x)
--R
--R
--R             x
--R           ++          %A
--R   (310)   |   ----------------- d%A
--R          ++     2%A      %A
--R               %e    + 3%e   + 3
--R                                         Type: Union(Expression(Integer),...)
--E 346
--S 347 of 578
m0067:= a0067-r0067
--R
--R
--R             x
--R           ++          %A
--R   (311)   |   ----------------- d%A  - r0067
--R          ++     2%A      %A
--R               %e    + 3%e   + 3
--R                                                    Type: Expression(Integer)
--E 347
--S 348 of 578
d0067:= D(m0067,x)
--R
--R
--R                 x
--R   (312)  ---------------
--R            2x      x
--R          %e   + 3%e  + 3
--R                                                    Type: Expression(Integer)
--E 348
--S 349 of 578

t0068:= x/(a+b*exp(x)+c*exp(1)^(2*x))
--R
--R
--R                   x
--R   (313)  ------------------
--R              2x       x
--R          c %e   + b %e  + a
--R                                                    Type: Expression(Integer)
--E 349
--S 350 of 578
r0068:= c*x^2/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_
        c*x^2/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_
        2*c*x*log(1+2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/_
        (b-(b^2-4*a*c)^(1/2))+2*c*x*log(1+2*c*exp(x)/_
        (b+(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_
        2*c*polylog(2,-2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))+_
        2*c*polylog(2,-2*c*exp(x)/(b+(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 350
--S 351 of 578
a0068:= integrate(t0068,x)
--R
--R
--R             x
--R           ++           %A
--R   (314)   |   -------------------- d%A
--R          ++       2%A       %A
--R               c %e    + b %e   + a
--R                                         Type: Union(Expression(Integer),...)
--E 351
--S 352 of 578
m0068:= a0068-r0068

--R
--R
--R             x
--R           ++           %A
--R   (315)   |   -------------------- d%A  - r0068
--R          ++       2%A       %A
--R               c %e    + b %e   + a
--R                                                    Type: Expression(Integer)
--E 352
--S 353 of 578
d0068:= D(m0068,x)
--R
--R
--R                   x
--R   (316)  ------------------
--R              2x       x
--R          c %e   + b %e  + a
--R                                                    Type: Expression(Integer)
--E 353
--S 354 of 578
t0069:= x^2/(-1+exp(x)+exp(1)^(2*x))
--R
--R
--R                 2
--R                x
--R   (317)  --------------
--R            2x     x
--R          %e   + %e  - 1
--R                                                    Type: Expression(Integer)
--E 354
--S 355 of 578
r0069:= 2/15*x^3*5^(1/2)/(1-5^(1/2))-2/15*x^3*5^(1/2)/(5^(1/2)+1)-_
        2/5*x^2*log(1+2*exp(x)/(1-5^(1/2)))*5^(1/2)/(1-5^(1/2))+_
        2/5*x^2*log(1+2*exp(x)/(5^(1/2)+1))*5^(1/2)/(5^(1/2)+1)-_
        4/5*x*polylog(2,-2*exp(x)/(1-5^(1/2)))*5^(1/2)/(1-5^(1/2))+_
        4/5*x*polylog(2,-2*exp(x)/(5^(1/2)+1))*5^(1/2)/(5^(1/2)+1)+_
        4/5*polylog(3,-2*exp(x)/(1-5^(1/2)))*5^(1/2)/(1-5^(1/2))-_
        4/5*polylog(3,-2*exp(x)/(5^(1/2)+1))*5^(1/2)/(5^(1/2)+1)
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)

--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 355
--S 356 of 578
a0069:= integrate(t0069,x)
--R
--R
--R             x          2
--R           ++         %A
--R   (318)   |   ---------------- d%A
--R          ++     2%A     %A
--R               %e    + %e   - 1
--R                                         Type: Union(Expression(Integer),...)
--E 356
--S 357 of 578
m0069:= a0069-r0069
--R
--R
--R             x          2
--R           ++         %A
--R   (319)   |   ---------------- d%A  - r0069
--R          ++     2%A     %A
--R               %e    + %e   - 1
--R                                                    Type: Expression(Integer)
--E 357
--S 358 of 578
d0069:= D(m0069,x)
--R
--R
--R                 2
--R                x
--R   (320)  --------------
--R            2x     x
--R          %e   + %e  - 1
--R                                                    Type: Expression(Integer)
--E 358
--S 359 of 578
t0070:= x^2/(3+3*exp(x)+exp(1)^(2*x))
--R
--R
--R                  2
--R                 x
--R   (321)  ---------------

--R            2x      x
--R          %e   + 3%e  + 3
--R                                                    Type: Expression(Integer)
--E 359
--S 360 of 578
r0070:= -2/9*%i*x^3*3^(1/2)/(3-%i*3^(1/2))+2/9*%i*x^3*3^(1/2)/(3+%i*3^(1/2))+_
        2/3*%i*x^2*log(1+2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_
        2/3*%i*x^2*log(1+2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))+_
        4/3*%i*x*polylog(2,-2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_
        4/3*%i*x*polylog(2,-2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))-_
        4/3*%i*polylog(3,-2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))+_
        4/3*%i*polylog(3,-2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                        Expression(Complex(Integer))
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 360
--S 361 of 578
a0070:= integrate(t0070,x)
--R
--R
--R             x          2
--R           ++         %A
--R   (322)   |   ----------------- d%A
--R          ++     2%A      %A
--R               %e    + 3%e   + 3
--R                                         Type: Union(Expression(Integer),...)
--E 361
--S 362 of 578
m0070:= a0070-r0070
--R
--R
--R             x          2
--R           ++         %A
--R   (323)   |   ----------------- d%A  - r0070
--R          ++     2%A      %A
--R               %e    + 3%e   + 3

--S 363 of 578
d0070:= D(m0070,x)
--R
--R
--R                  2
--R                 x
--R   (324)  ---------------
--R            2x      x
--R          %e   + 3%e  + 3
--R                                                    Type: Expression(Integer)
--E 363
--S 364 of 578
t0071:= x^2/(a+b*exp(x)+c*exp(1)^(2*x))
--R
--R
--R                   2
--R                  x
--R   (325)  ------------------
--R              2x       x
--R          c %e   + b %e  + a
--R                                                    Type: Expression(Integer)
--E 364
--S 365 of 578
r0071:= 2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_
        2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_
        2*c*x^2*log(1+2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))+2*c*x^2*log(1+2*c*exp(x)/_
        (b+(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_
        4*c*x*polylog(2,-2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))+_
        4*c*x*polylog(2,-2*c*exp(x)/(b+(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))+_
        4*c*polylog(3,-2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_
        4*c*polylog(3,-2*c*exp(x)/(b+(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)

--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 365
--S 366 of 578
a0071:= integrate(t0071,x)
--R
--R
--R             x            2
--R           ++           %A
--R   (326)   |   -------------------- d%A
--R          ++       2%A       %A
--R               c %e    + b %e   + a
--R                                         Type: Union(Expression(Integer),...)
--E 366
--S 367 of 578
m0071:= a0071-r0071
--R
--R
--R             x            2
--R           ++           %A
--R   (327)   |   -------------------- d%A  - r0071
--R          ++       2%A       %A
--R               c %e    + b %e   + a
--R                                                    Type: Expression(Integer)
--E 367
--S 368 of 578
d0071:= D(m0071,x)
--R
--R
--R                   2
--R                  x
--R   (328)  ------------------
--R              2x       x
--R          c %e   + b %e  + a
--R                                                    Type: Expression(Integer)
--E 368
--S 369 of 578
t0072:= 1/(1+2*f^(c+d*x)+f^(2*c+2*d*x))
--R
--R
--R                       1
--R   (329)  --------------------------
--R           2d x + 2c     d x + c

--R          f          + 2f        + 1
--R                                                    Type: Expression(Integer)
--E 369
--S 370 of 578
r0072:= x+1/d/(1+f^(c+d*x))/log(f)-log(1+f^(c+d*x))/d/log(f)
--R
--R
--R   (330)
--R       d x + c          d x + c                   d x + c
--R   (- f        - 1)log(f        + 1) + d x log(f)f        + d x log(f) + 1
--R   -----------------------------------------------------------------------
--R                                  d x + c
--R                         d log(f)f        + d log(f)
--R                                                    Type: Expression(Integer)
--E 370
--S 371 of 578
a0072:= integrate(t0072,x)
--R
--R
--R   (331)
--R            (d x + c)log(f)           (d x + c)log(f)
--R       (- %e                - 1)log(%e                + 1)
--R     +
--R                   (d x + c)log(f)
--R       d x log(f)%e                + d x log(f) + 1
--R  /
--R               (d x + c)log(f)
--R     d log(f)%e                + d log(f)
--R                                         Type: Union(Expression(Integer),...)
--E 371
--S 372 of 578
m0072:= a0072-r0072
--R
--R
--R   (332)
--R              d x + c       (d x + c)log(f)    d x + c
--R         ((- f        - 1)%e                - f        - 1)
--R      *
--R               (d x + c)log(f)
--R         log(%e                + 1)
--R     +
--R          d x + c       (d x + c)log(f)    d x + c          d x + c
--R       ((f        + 1)%e                + f        + 1)log(f        + 1)
--R     +
--R           (d x + c)log(f)    d x + c
--R       - %e                + f
--R  /

--R                 d x + c              (d x + c)log(f)            d x + c
--R       (d log(f)f        + d log(f))%e                + d log(f)f
--R     +
--R       d log(f)
--R                                                    Type: Expression(Integer)
--E 372
--S 373 of 578
d0072:= D(m0072,x)
--R
--R
--R   (333)
--R          (d x + c)log(f) 2      (d x + c)log(f)     d x + c 2     d x + c
--R     - (%e               )  - 2%e                + (f       )  + 2f
--R  /
--R          d x + c 2     d x + c        (d x + c)log(f) 2
--R       ((f       )  + 2f        + 1)(%e               )
--R     +
--R           d x + c 2     d x + c       (d x + c)log(f)     d x + c 2     d x + c
--R       (2(f       )  + 4f        + 2)%e                + (f       )  + 2f
--R     +
--R       1
--R                                                    Type: Expression(Integer)
--E 373
--S 374 of 578
t0073:= 1/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x))
--R
--R
--R                        1
--R   (334)  -----------------------------
--R             2d x + 2c      d x + c
--R          c f          + b f        + a
--R                                                    Type: Expression(Integer)
--E 374
--S 375 of 578
r0073:= x/a+b*arctanh((b+2*c*f^(c+d*x))/(b^2-4*a*c)^(1/2))/a/_
        (b^2-4*a*c)^(1/2)/d/log(f)-1/2*log(a+b*f^(c+d*x)+_
        c*f^(2*c+2*d*x))/a/d/log(f)
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)

--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 375
--S 376 of 578
a0073:= integrate(t0073,x)
--R
--R
--R   (335)
--R   [
--R            +-----------+
--R            |          2          (d x + c)log(f) 2       (d x + c)log(f)
--R         - \|- 4a c + b  log(c (%e               )  + b %e                + a)
--R       +
--R           b
--R        *
--R           log
--R                      +-----------+
--R                    2 |          2    (d x + c)log(f) 2
--R                  2c \|- 4a c + b  (%e               )
--R                +
--R                        +-----------+
--R                        |          2        2     2    (d x + c)log(f)
--R                  (2b c\|- 4a c + b   - 8a c  + 2b c)%e
--R                +
--R                                +-----------+
--R                             2  |          2              3
--R                  (- 2a c + b )\|- 4a c + b   - 4a b c + b
--R             /
--R                     (d x + c)log(f) 2       (d x + c)log(f)
--R                c (%e               )  + b %e                + a
--R       +
--R                     +-----------+
--R                     |          2
--R         2d x log(f)\|- 4a c + b
--R    /
--R                   +-----------+
--R                   |          2
--R       2a d log(f)\|- 4a c + b
--R     ,
--R
--R            +---------+
--R            |        2          (d x + c)log(f) 2       (d x + c)log(f)
--R         - \|4a c - b  log(c (%e               )  + b %e                + a)
--R       +
--R                      +---------+                      +---------+
--R                      |        2   (d x + c)log(f)     |        2
--R                   2c\|4a c - b  %e                + b\|4a c - b
--R         - 2b atan(-----------------------------------------------)

--R                                              2
--R                                      4a c - b
--R       +
--R                     +---------+
--R                     |        2
--R         2d x log(f)\|4a c - b
--R    /
--R                   +---------+
--R                   |        2
--R       2a d log(f)\|4a c - b
--R     ]
--R                                   Type: Union(List(Expression(Integer)),...)
--E 376
--S 377 of 578
m0073:= a0073-r0073
--R
--R   There are 12 exposed and 3 unexposed library operations named -
--R      having 2 argument(s) but none was determined to be applicable.
--R      Use HyperDoc Browse, or issue
--R                                )display op -
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--R   Cannot find a definition or applicable library operation named -
--R      with argument type(s)
--R                          List(Expression(Integer))
--R                               Variable(r0073)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 377
--S 378 of 578
d0073:= D(m0073,x)
--R
--R
--R   (336)  0
--R                                                    Type: Polynomial(Integer)
--E 378
--S 379 of 578
t0074:= x/(1+2*f^(c+d*x)+f^(2*c+2*d*x))
--R
--R
--R                       x
--R   (337)  --------------------------
--R           2d x + 2c     d x + c
--R          f          + 2f        + 1

--S 380 of 578
r0074:= 1/2*x^2-x/d/log(f)+log(1+f^(c+d*x))/d^2/log(f)^2+_
        x*(1/d/(1+f^(c+d*x))/log(f)-log(1+f^(c+d*x))/d/log(f))-_
        polylog(2,-f^(c+d*x))/d^2/log(f)^2
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 380
--S 381 of 578
a0074:= integrate(t0074,x)
--R
--R
--R             x
--R           ++               %A
--R   (338)   |   ---------------------------- d%A
--R          ++    2%A d + 2c     %A d + c
--R               f           + 2f         + 1
--R                                         Type: Union(Expression(Integer),...)
--E 381
--S 382 of 578
m0074:= a0074-r0074
--R
--R
--R             x
--R           ++               %A
--R   (339)   |   ---------------------------- d%A  - r0074
--R          ++    2%A d + 2c     %A d + c
--R               f           + 2f         + 1
--R                                                    Type: Expression(Integer)
--E 382
--S 383 of 578
d0074:= D(m0074,x)
--R

--R
--R                       x
--R   (340)  --------------------------
--R           2d x + 2c     d x + c
--R          f          + 2f        + 1
--R                                                    Type: Expression(Integer)
--E 383
--S 384 of 578
t0075:= x/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x))
--R
--R
--R                        x
--R   (341)  -----------------------------
--R             2d x + 2c      d x + c
--R          c f          + b f        + a
--R                                                    Type: Expression(Integer)
--E 384
--S 385 of 578
r0075:= c*x^2/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_
        c*x^2/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_
        2*c*x*log(1+2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d/log(f)+_
        2*c*x*log(1+2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d/log(f)-_
        2*c*polylog(2,-2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d^2/log(f)^2+_
        2*c*polylog(2,-2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d^2/log(f)^2
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 385
--S 386 of 578
a0075:= integrate(t0075,x)
--R
--R

--R             x
--R           ++                 %A
--R   (342)   |   ------------------------------- d%A
--R          ++      2%A d + 2c      %A d + c
--R               c f           + b f         + a
--R                                         Type: Union(Expression(Integer),...)
--E 386
--S 387 of 578
m0075:= a0075-r0075
--R
--R
--R             x
--R           ++                 %A
--R   (343)   |   ------------------------------- d%A  - r0075
--R          ++      2%A d + 2c      %A d + c
--R               c f           + b f         + a
--R                                                    Type: Expression(Integer)
--E 387
--S 388 of 578
d0075:= D(m0075,x)
--R
--R
--R                        x
--R   (344)  -----------------------------
--R             2d x + 2c      d x + c
--R          c f          + b f        + a
--R                                                    Type: Expression(Integer)
--E 388
--S 389 of 578
t0076:= x^2/(1+2*f^(c+d*x)+f^(2*c+2*d*x))
--R
--R
--R                       2
--R                      x
--R   (345)  --------------------------
--R           2d x + 2c     d x + c
--R          f          + 2f        + 1
--R                                                    Type: Expression(Integer)
--E 389
--S 390 of 578
r0076:= 1/3*x^3-x^2/d/log(f)+2*x*log(1+f^(c+d*x))/d^2/log(f)^2+_
        x^2*(1/d/(1+f^(c+d*x))/log(f)-log(1+f^(c+d*x))/d/log(f))+_
        2*(1-d*x*log(f))*polylog(2,-f^(c+d*x))/d^3/log(f)^3+_
        2*polylog(3,-f^(c+d*x))/d^3/log(f)^3
--R
--R   There are no library operations named polylog

--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 390
--S 391 of 578
a0076:= integrate(t0076,x)
--R
--R
--R             x                2
--R           ++               %A
--R   (346)   |   ---------------------------- d%A
--R          ++    2%A d + 2c     %A d + c
--R               f           + 2f         + 1
--R                                         Type: Union(Expression(Integer),...)
--E 391
--S 392 of 578
m0076:= a0076-r0076
--R
--R
--R             x                2
--R           ++               %A
--R   (347)   |   ---------------------------- d%A  - r0076
--R          ++    2%A d + 2c     %A d + c
--R               f           + 2f         + 1
--R                                                    Type: Expression(Integer)
--E 392
--S 393 of 578
d0076:= D(m0076,x)
--R
--R
--R                       2
--R                      x
--R   (348)  --------------------------
--R           2d x + 2c     d x + c
--R          f          + 2f        + 1
--R                                                    Type: Expression(Integer)
--E 393

--S 394 of 578
t0077:= x^2/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x))
--R
--R
--R                         2
--R                        x
--R   (349)  -----------------------------
--R             2d x + 2c      d x + c
--R          c f          + b f        + a
--R                                                    Type: Expression(Integer)
--E 394
--S 395 of 578
r0077:= 2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_
        2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_
        2*c*x^2*log(1+2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d/log(f)+_
        2*c*x^2*log(1+2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d/log(f)-_
        4*c*x*polylog(2,-2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d^2/log(f)^2+_
        4*c*x*polylog(2,-2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d^2/log(f)^2+_
        4*c*polylog(3,-2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d^3/log(f)^3-_
        4*c*polylog(3,-2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_
        (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d^3/log(f)^3
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 395
--S 396 of 578
a0077:= integrate(t0077,x)
--R
--R
--R             x                 2
--R           ++                %A
--R   (350)   |   ------------------------------- d%A

--R          ++      2%A d + 2c      %A d + c
--R               c f           + b f         + a
--R                                         Type: Union(Expression(Integer),...)
--E 396
--S 397 of 578
m0077:= a0077-r0077
--R
--R
--R             x                 2
--R           ++                %A
--R   (351)   |   ------------------------------- d%A  - r0077
--R          ++      2%A d + 2c      %A d + c
--R               c f           + b f         + a
--R                                                    Type: Expression(Integer)
--E 397
--S 398 of 578
d0077:= D(m0077,x)
--R
--R
--R                         2
--R                        x
--R   (352)  -----------------------------
--R             2d x + 2c      d x + c
--R          c f          + b f        + a
--R                                                    Type: Expression(Integer)
--E 398
--S 399 of 578
t0078:= 1/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x))
--R
--R
--R                        1
--R   (353)  -----------------------------
--R             2h x + 2g      h x + g
--R          c f          + b f        + a
--R                                                    Type: Expression(Integer)
--E 399
--S 400 of 578
r0078:= x/a+b*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/a/_
        (b^2-4*a*c)^(1/2)/h/log(f)-1/2*log(a+b*f^(g+h*x)+_
        c*f^(2*g+2*h*x))/a/h/log(f)
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.

--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 400
--S 401 of 578
a0078:= integrate(t0078,x)
--R
--R
--R   (354)
--R   [
--R            +-----------+
--R            |          2          (h x + g)log(f) 2       (h x + g)log(f)
--R         - \|- 4a c + b  log(c (%e               )  + b %e                + a)
--R       +
--R           b
--R        *
--R           log
--R                      +-----------+
--R                    2 |          2    (h x + g)log(f) 2
--R                  2c \|- 4a c + b  (%e               )
--R                +
--R                        +-----------+
--R                        |          2        2     2    (h x + g)log(f)
--R                  (2b c\|- 4a c + b   - 8a c  + 2b c)%e
--R                +
--R                                +-----------+
--R                             2  |          2              3
--R                  (- 2a c + b )\|- 4a c + b   - 4a b c + b
--R             /
--R                     (h x + g)log(f) 2       (h x + g)log(f)
--R                c (%e               )  + b %e                + a
--R       +
--R                     +-----------+
--R                     |          2
--R         2h x log(f)\|- 4a c + b
--R    /
--R                   +-----------+
--R                   |          2
--R       2a h log(f)\|- 4a c + b
--R     ,
--R
--R            +---------+
--R            |        2          (h x + g)log(f) 2       (h x + g)log(f)
--R         - \|4a c - b  log(c (%e               )  + b %e                + a)
--R       +

--R                      +---------+                      +---------+
--R                      |        2   (h x + g)log(f)     |        2
--R                   2c\|4a c - b  %e                + b\|4a c - b
--R         - 2b atan(-----------------------------------------------)
--R                                              2
--R                                      4a c - b
--R       +
--R                     +---------+
--R                     |        2
--R         2h x log(f)\|4a c - b
--R    /
--R                   +---------+
--R                   |        2
--R       2a h log(f)\|4a c - b
--R     ]
--R                                   Type: Union(List(Expression(Integer)),...)
--E 401
--S 402 of 578
m0078a:= a0078.1-r0078
--R
--R
--R   (355)
--R          +-----------+
--R          |          2          (h x + g)log(f) 2       (h x + g)log(f)
--R       - \|- 4a c + b  log(c (%e               )  + b %e                + a)
--R     +
--R         b
--R      *
--R         log
--R                    +-----------+
--R                  2 |          2    (h x + g)log(f) 2
--R                2c \|- 4a c + b  (%e               )
--R              +
--R                      +-----------+
--R                      |          2        2     2    (h x + g)log(f)
--R                (2b c\|- 4a c + b   - 8a c  + 2b c)%e
--R              +
--R                              +-----------+
--R                           2  |          2              3
--R                (- 2a c + b )\|- 4a c + b   - 4a b c + b
--R           /
--R                   (h x + g)log(f) 2       (h x + g)log(f)
--R              c (%e               )  + b %e                + a
--R     +
--R                                 +-----------+
--R                                 |          2
--R       (2h x - 2a h r0078)log(f)\|- 4a c + b
--R  /
--R                 +-----------+

--R                 |          2
--R     2a h log(f)\|- 4a c + b
--R                                                    Type: Expression(Integer)
--E 402
--S 403 of 578
d0078a:= D(m0078a,x)
--R
--R
--R                                  1
--R   (356)  ------------------------------------------------
--R               (h x + g)log(f) 2       (h x + g)log(f)
--R          c (%e               )  + b %e                + a
--R                                                    Type: Expression(Integer)
--E 403
--S 404 of 578
m0078b:= a0078.2-r0078
--R
--R
--R   (357)
--R          +---------+
--R          |        2          (h x + g)log(f) 2       (h x + g)log(f)
--R       - \|4a c - b  log(c (%e               )  + b %e                + a)
--R     +
--R                    +---------+                      +---------+
--R                    |        2   (h x + g)log(f)     |        2
--R                 2c\|4a c - b  %e                + b\|4a c - b
--R       - 2b atan(-----------------------------------------------)
--R                                            2
--R                                    4a c - b
--R     +
--R                                 +---------+
--R                                 |        2
--R       (2h x - 2a h r0078)log(f)\|4a c - b
--R  /
--R                 +---------+
--R                 |        2
--R     2a h log(f)\|4a c - b
--R                                                    Type: Expression(Integer)
--E 404
--S 405 of 578
d0078b:= D(m0078b,x)
--R
--R
--R                                  1
--R   (358)  ------------------------------------------------
--R               (h x + g)log(f) 2       (h x + g)log(f)
--R          c (%e               )  + b %e                + a

--S 406 of 578
t0079:= 1/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x))
--R
--R
--R                        1
--R   (359)  -----------------------------
--R             2h x + 2g      h x + g
--R          c f          + b f        + a
--R                                                    Type: Expression(Integer)
--E 406
--S 407 of 578
r0079:= x/a+b*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/a/_
        (b^2-4*a*c)^(1/2)/h/log(f)-1/2*log(a+b*f^(g+h*x)+_
        c*f^(2*g+2*h*x))/a/h/log(f)
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 407
--S 408 of 578
a0079:= integrate(t0079,x)
--R
--R
--R   (360)
--R   [
--R            +-----------+
--R            |          2          (h x + g)log(f) 2       (h x + g)log(f)
--R         - \|- 4a c + b  log(c (%e               )  + b %e                + a)
--R       +
--R           b
--R        *
--R           log
--R                      +-----------+
--R                    2 |          2    (h x + g)log(f) 2
--R                  2c \|- 4a c + b  (%e               )
--R                +

--R                        +-----------+
--R                        |          2        2     2    (h x + g)log(f)
--R                  (2b c\|- 4a c + b   - 8a c  + 2b c)%e
--R                +
--R                                +-----------+
--R                             2  |          2              3
--R                  (- 2a c + b )\|- 4a c + b   - 4a b c + b
--R             /
--R                     (h x + g)log(f) 2       (h x + g)log(f)
--R                c (%e               )  + b %e                + a
--R       +
--R                     +-----------+
--R                     |          2
--R         2h x log(f)\|- 4a c + b
--R    /
--R                   +-----------+
--R                   |          2
--R       2a h log(f)\|- 4a c + b
--R     ,
--R
--R            +---------+
--R            |        2          (h x + g)log(f) 2       (h x + g)log(f)
--R         - \|4a c - b  log(c (%e               )  + b %e                + a)
--R       +
--R                      +---------+                      +---------+
--R                      |        2   (h x + g)log(f)     |        2
--R                   2c\|4a c - b  %e                + b\|4a c - b
--R         - 2b atan(-----------------------------------------------)
--R                                              2
--R                                      4a c - b
--R       +
--R                     +---------+
--R                     |        2
--R         2h x log(f)\|4a c - b
--R    /
--R                   +---------+
--R                   |        2
--R       2a h log(f)\|4a c - b
--R     ]
--R                                   Type: Union(List(Expression(Integer)),...)
--E 408
--S 409 of 578
m0079a:= a0079.1-r0079
--R
--R
--R   (361)
--R          +-----------+
--R          |          2          (h x + g)log(f) 2       (h x + g)log(f)
--R       - \|- 4a c + b  log(c (%e               )  + b %e                + a)

--R     +
--R         b
--R      *
--R         log
--R                    +-----------+
--R                  2 |          2    (h x + g)log(f) 2
--R                2c \|- 4a c + b  (%e               )
--R              +
--R                      +-----------+
--R                      |          2        2     2    (h x + g)log(f)
--R                (2b c\|- 4a c + b   - 8a c  + 2b c)%e
--R              +
--R                              +-----------+
--R                           2  |          2              3
--R                (- 2a c + b )\|- 4a c + b   - 4a b c + b
--R           /
--R                   (h x + g)log(f) 2       (h x + g)log(f)
--R              c (%e               )  + b %e                + a
--R     +
--R                                 +-----------+
--R                                 |          2
--R       (2h x - 2a h r0079)log(f)\|- 4a c + b
--R  /
--R                 +-----------+
--R                 |          2
--R     2a h log(f)\|- 4a c + b
--R                                                    Type: Expression(Integer)
--E 409
--S 410 of 578
d0079a:= D(m0079a,x)
--R
--R
--R                                  1
--R   (362)  ------------------------------------------------
--R               (h x + g)log(f) 2       (h x + g)log(f)
--R          c (%e               )  + b %e                + a
--R                                                    Type: Expression(Integer)
--E 410
--S 411 of 578
m0079b:= a0079.2-r0079
--R
--R
--R   (363)
--R          +---------+
--R          |        2          (h x + g)log(f) 2       (h x + g)log(f)
--R       - \|4a c - b  log(c (%e               )  + b %e                + a)
--R     +
--R                    +---------+                      +---------+

--R                    |        2   (h x + g)log(f)     |        2
--R                 2c\|4a c - b  %e                + b\|4a c - b
--R       - 2b atan(-----------------------------------------------)
--R                                            2
--R                                    4a c - b
--R     +
--R                                 +---------+
--R                                 |        2
--R       (2h x - 2a h r0079)log(f)\|4a c - b
--R  /
--R                 +---------+
--R                 |        2
--R     2a h log(f)\|4a c - b
--R                                                    Type: Expression(Integer)
--E 411
--S 412 of 578
d0079b:= D(m0079b,x)
--R
--R
--R                                  1
--R   (364)  ------------------------------------------------
--R               (h x + g)log(f) 2       (h x + g)log(f)
--R          c (%e               )  + b %e                + a
--R                                                    Type: Expression(Integer)
--E 412
--S 413 of 578
t0080:= (d+e*f^(g+h*x))/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x))
--R
--R
--R                     h x + g
--R                  e f        + d
--R   (365)  -----------------------------
--R             2h x + 2g      h x + g
--R          c f          + b f        + a
--R                                                    Type: Expression(Integer)
--E 413
--S 414 of 578
r0080:= d*x/a+(b*d-2*a*e)*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/_
        a/(b^2-4*a*c)^(1/2)/h/log(f)-1/2*d*log(a+b*f^(g+h*x)+_
        c*f^(2*g+2*h*x))/a/h/log(f)
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R

--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 414
--S 415 of 578
a0080:= integrate(t0080,x)
--R
--R
--R   (366)
--R   [
--R             +-----------+
--R             |          2          (h x + g)log(f) 2       (h x + g)log(f)
--R         - d\|- 4a c + b  log(c (%e               )  + b %e                + a)
--R       +
--R           (2a e - b d)
--R        *
--R           log
--R                      +-----------+
--R                    2 |          2    (h x + g)log(f) 2
--R                  2c \|- 4a c + b  (%e               )
--R                +
--R                        +-----------+
--R                        |          2        2     2    (h x + g)log(f)
--R                  (2b c\|- 4a c + b   + 8a c  - 2b c)%e
--R                +
--R                                +-----------+
--R                             2  |          2              3
--R                  (- 2a c + b )\|- 4a c + b   + 4a b c - b
--R             /
--R                     (h x + g)log(f) 2       (h x + g)log(f)
--R                c (%e               )  + b %e                + a
--R       +
--R                       +-----------+
--R                       |          2
--R         2d h x log(f)\|- 4a c + b
--R    /
--R                   +-----------+
--R                   |          2
--R       2a h log(f)\|- 4a c + b
--R     ,
--R
--R             +---------+
--R             |        2          (h x + g)log(f) 2       (h x + g)log(f)
--R         - d\|4a c - b  log(c (%e               )  + b %e                + a)
--R       +
--R                              +---------+                      +---------+

--R                              |        2   (h x + g)log(f)     |        2
--R                           2c\|4a c - b  %e                + b\|4a c - b
--R         (4a e - 2b d)atan(-----------------------------------------------)
--R                                                      2
--R                                              4a c - b
--R       +
--R                       +---------+
--R                       |        2
--R         2d h x log(f)\|4a c - b
--R    /
--R                   +---------+
--R                   |        2
--R       2a h log(f)\|4a c - b
--R     ]
--R                                   Type: Union(List(Expression(Integer)),...)
--E 415
--S 416 of 578
m0080a:= a0080.1-r0080
--R
--R
--R   (367)
--R           +-----------+
--R           |          2          (h x + g)log(f) 2       (h x + g)log(f)
--R       - d\|- 4a c + b  log(c (%e               )  + b %e                + a)
--R     +
--R         (2a e - b d)
--R      *
--R         log
--R                    +-----------+
--R                  2 |          2    (h x + g)log(f) 2
--R                2c \|- 4a c + b  (%e               )
--R              +
--R                      +-----------+
--R                      |          2        2     2    (h x + g)log(f)
--R                (2b c\|- 4a c + b   + 8a c  - 2b c)%e
--R              +
--R                              +-----------+
--R                           2  |          2              3
--R                (- 2a c + b )\|- 4a c + b   + 4a b c - b
--R           /
--R                   (h x + g)log(f) 2       (h x + g)log(f)
--R              c (%e               )  + b %e                + a
--R     +
--R                                   +-----------+
--R                                   |          2
--R       (2d h x - 2a h r0080)log(f)\|- 4a c + b
--R  /
--R                 +-----------+
--R                 |          2

--R     2a h log(f)\|- 4a c + b
--R                                                    Type: Expression(Integer)
--E 416
--S 417 of 578
d0080a:= D(m0080a,x)
--R
--R
--R                           (h x + g)log(f)
--R                       e %e                + d
--R   (368)  ------------------------------------------------
--R               (h x + g)log(f) 2       (h x + g)log(f)
--R          c (%e               )  + b %e                + a
--R                                                    Type: Expression(Integer)
--E 417
--S 418 of 578
m0080b:= a0080.2-r0080
--R
--R
--R   (369)
--R           +---------+
--R           |        2          (h x + g)log(f) 2       (h x + g)log(f)
--R       - d\|4a c - b  log(c (%e               )  + b %e                + a)
--R     +
--R                            +---------+                      +---------+
--R                            |        2   (h x + g)log(f)     |        2
--R                         2c\|4a c - b  %e                + b\|4a c - b
--R       (4a e - 2b d)atan(-----------------------------------------------)
--R                                                    2
--R                                            4a c - b
--R     +
--R                                   +---------+
--R                                   |        2
--R       (2d h x - 2a h r0080)log(f)\|4a c - b
--R  /
--R                 +---------+
--R                 |        2
--R     2a h log(f)\|4a c - b
--R                                                    Type: Expression(Integer)
--E 418
--S 419 of 578
d0080b:= D(m0080b,x)
--R
--R
--R                           (h x + g)log(f)
--R                       e %e                + d
--R   (370)  ------------------------------------------------
--R               (h x + g)log(f) 2       (h x + g)log(f)

--R          c (%e               )  + b %e                + a
--R                                                    Type: Expression(Integer)
--E 419
--S 420 of 578
t0081:= (d+e*f^(g+h*x))/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x))
--R
--R
--R                     h x + g
--R                  e f        + d
--R   (371)  -----------------------------
--R             2h x + 2g      h x + g
--R          c f          + b f        + a
--R                                                    Type: Expression(Integer)
--E 420
--S 421 of 578
r0081:= d*x/a+(b*d-2*a*e)*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/_
        a/(b^2-4*a*c)^(1/2)/h/log(f)-1/2*d*log(a+b*f^(g+h*x)+_
        c*f^(2*g+2*h*x))/a/h/log(f)
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 421
--S 422 of 578
a0081:= integrate(t0081,x)
--R
--R
--R   (372)
--R   [
--R             +-----------+
--R             |          2          (h x + g)log(f) 2       (h x + g)log(f)
--R         - d\|- 4a c + b  log(c (%e               )  + b %e                + a)
--R       +
--R           (2a e - b d)
--R        *
--R           log
--R                      +-----------+
--R                    2 |          2    (h x + g)log(f) 2

--R                  2c \|- 4a c + b  (%e               )
--R                +
--R                        +-----------+
--R                        |          2        2     2    (h x + g)log(f)
--R                  (2b c\|- 4a c + b   + 8a c  - 2b c)%e
--R                +
--R                                +-----------+
--R                             2  |          2              3
--R                  (- 2a c + b )\|- 4a c + b   + 4a b c - b
--R             /
--R                     (h x + g)log(f) 2       (h x + g)log(f)
--R                c (%e               )  + b %e                + a
--R       +
--R                       +-----------+
--R                       |          2
--R         2d h x log(f)\|- 4a c + b
--R    /
--R                   +-----------+
--R                   |          2
--R       2a h log(f)\|- 4a c + b
--R     ,
--R
--R             +---------+
--R             |        2          (h x + g)log(f) 2       (h x + g)log(f)
--R         - d\|4a c - b  log(c (%e               )  + b %e                + a)
--R       +
--R                              +---------+                      +---------+
--R                              |        2   (h x + g)log(f)     |        2
--R                           2c\|4a c - b  %e                + b\|4a c - b
--R         (4a e - 2b d)atan(-----------------------------------------------)
--R                                                      2
--R                                              4a c - b
--R       +
--R                       +---------+
--R                       |        2
--R         2d h x log(f)\|4a c - b
--R    /
--R                   +---------+
--R                   |        2
--R       2a h log(f)\|4a c - b
--R     ]
--R                                   Type: Union(List(Expression(Integer)),...)
--E 422
--S 423 of 578
m0081a:= a0081.1-r0081
--R
--R
--R   (373)
--R           +-----------+

--R           |          2          (h x + g)log(f) 2       (h x + g)log(f)
--R       - d\|- 4a c + b  log(c (%e               )  + b %e                + a)
--R     +
--R         (2a e - b d)
--R      *
--R         log
--R                    +-----------+
--R                  2 |          2    (h x + g)log(f) 2
--R                2c \|- 4a c + b  (%e               )
--R              +
--R                      +-----------+
--R                      |          2        2     2    (h x + g)log(f)
--R                (2b c\|- 4a c + b   + 8a c  - 2b c)%e
--R              +
--R                              +-----------+
--R                           2  |          2              3
--R                (- 2a c + b )\|- 4a c + b   + 4a b c - b
--R           /
--R                   (h x + g)log(f) 2       (h x + g)log(f)
--R              c (%e               )  + b %e                + a
--R     +
--R                                   +-----------+
--R                                   |          2
--R       (2d h x - 2a h r0081)log(f)\|- 4a c + b
--R  /
--R                 +-----------+
--R                 |          2
--R     2a h log(f)\|- 4a c + b
--R                                                    Type: Expression(Integer)
--E 423
--S 424 of 578
d0081a:= D(m0081a,x)
--R
--R
--R                           (h x + g)log(f)
--R                       e %e                + d
--R   (374)  ------------------------------------------------
--R               (h x + g)log(f) 2       (h x + g)log(f)
--R          c (%e               )  + b %e                + a
--R                                                    Type: Expression(Integer)
--E 424
--S 425 of 578
m0081b:= a0081.2-r0081
--R
--R
--R   (375)
--R           +---------+
--R           |        2          (h x + g)log(f) 2       (h x + g)log(f)

--R       - d\|4a c - b  log(c (%e               )  + b %e                + a)
--R     +
--R                            +---------+                      +---------+
--R                            |        2   (h x + g)log(f)     |        2
--R                         2c\|4a c - b  %e                + b\|4a c - b
--R       (4a e - 2b d)atan(-----------------------------------------------)
--R                                                    2
--R                                            4a c - b
--R     +
--R                                   +---------+
--R                                   |        2
--R       (2d h x - 2a h r0081)log(f)\|4a c - b
--R  /
--R                 +---------+
--R                 |        2
--R     2a h log(f)\|4a c - b
--R                                                    Type: Expression(Integer)
--E 425
--S 426 of 578
d0081b:= D(m0081b,x)
--R
--R
--R                           (h x + g)log(f)
--R                       e %e                + d
--R   (376)  ------------------------------------------------
--R               (h x + g)log(f) 2       (h x + g)log(f)
--R          c (%e               )  + b %e                + a
--R                                                    Type: Expression(Integer)
--E 426
--S 427 of 578
t0082:= x^2/(2+f^(-c-d*x)+f^(c+d*x))
--R
--R
--R                       2
--R                      x
--R   (377)  -------------------------
--R           d x + c    - d x - c
--R          f        + f          + 2
--R                                                    Type: Expression(Integer)
--E 427
--S 428 of 578
r0082:= x^2/d/log(f)-x^2/d/(1+f^(c+d*x))/log(f)-_
        2*x*log(1+f^(c+d*x))/d^2/log(f)^2-_
        2*polylog(2,-f^(c+d*x))/d^3/log(f)^3
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue

--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 428
--S 429 of 578
a0082:= integrate(t0082,x)
--R
--R
--R             x               2
--R           ++              %A
--R   (378)   |   --------------------------- d%A
--R          ++    %A d + c    - %A d - c
--R               f         + f           + 2
--R                                         Type: Union(Expression(Integer),...)
--E 429
--S 430 of 578
m0082:= a0082-r0082
--R
--R
--R             x               2
--R           ++              %A
--R   (379)   |   --------------------------- d%A  - r0082
--R          ++    %A d + c    - %A d - c
--R               f         + f           + 2
--R                                                    Type: Expression(Integer)
--E 430
--S 431 of 578
d0082:= D(m0082,x)
--R
--R
--R                       2
--R                      x
--R   (380)  -------------------------
--R           d x + c    - d x - c
--R          f        + f          + 2
--R                                                    Type: Expression(Integer)
--E 431
--S 432 of 578

t0083:= 1/(1-exp(1)^(-x)+2*exp(x))
--R
--R
--R                  1
--R   (381)  ----------------
--R             x     - x
--R          2%e  - %e    + 1
--R                                                    Type: Expression(Integer)
--E 432
--S 433 of 578
r0083:= -2/3*arctanh(1/3+4/3*exp(x))
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 433
--S 434 of 578
a0083:= integrate(t0083,x)
--R
--R
--R                 x              x
--R          log(2%e  - 1) - log(%e  + 1)
--R   (382)  ----------------------------
--R                        3
--R                                         Type: Union(Expression(Integer),...)
--E 434
--S 435 of 578
m0083:= a0083-r0083
--R
--R
--R                 x              x
--R          log(2%e  - 1) - log(%e  + 1) - 3r0083
--R   (383)  -------------------------------------
--R                            3
--R                                                    Type: Expression(Integer)
--E 435
--S 436 of 578

d0083:= D(m0083,x)
--R
--R
--R                   x
--R                 %e
--R   (384)  -----------------
--R              x 2     x
--R          2(%e )  + %e  - 1
--R                                                    Type: Expression(Integer)
--E 436
--S 437 of 578
t0084:= x^2/(a+b*exp(1)^(-x)+c*exp(x))
--R
--R
--R                    2
--R                   x
--R   (385)  -------------------
--R              x       - x
--R          c %e  + b %e    + a
--R                                                    Type: Expression(Integer)
--E 437
--S 438 of 578
r0084:= (x^2*log(-(a-(a^2-4*b*c)^(1/2)+2*c*exp(x))/(-a+(a^2-4*b*c)^(1/2)))-_
        x^2*log((a+(a^2-4*b*c)^(1/2)+2*c*exp(x))/(a+(a^2-4*b*c)^(1/2)))+_
        2*x*polylog(2,2*c*exp(x)/(-a+(a^2-4*b*c)^(1/2)))-_
        2*x*polylog(2,-2*c*exp(x)/(a+(a^2-4*b*c)^(1/2)))-_
        2*polylog(3,2*c*exp(x)/(-a+(a^2-4*b*c)^(1/2)))+_
        2*polylog(3,-2*c*exp(x)/(a+(a^2-4*b*c)^(1/2))))/(a^2-4*b*c)^(1/2)
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 438
--S 439 of 578
a0084:= integrate(t0084,x)
--R
--R

--R             x            2
--R           ++           %A
--R   (386)   |   --------------------- d%A
--R          ++       %A       - %A
--R               c %e   + b %e     + a
--R                                         Type: Union(Expression(Integer),...)
--E 439
--S 440 of 578
m0084:= a0084-r0084
--R
--R
--R             x            2
--R           ++           %A
--R   (387)   |   --------------------- d%A  - r0084
--R          ++       %A       - %A
--R               c %e   + b %e     + a
--R                                                    Type: Expression(Integer)
--E 440
--S 441 of 578
d0084:= D(m0084,x)
--R
--R
--R                    2
--R                   x
--R   (388)  -------------------
--R              x       - x
--R          c %e  + b %e    + a
--R                                                    Type: Expression(Integer)
--E 441
--S 442 of 578
t0085:= 1/(a+b*f^(-c-d*x)+c*f^(c+d*x))
--R
--R
--R                        1
--R   (389)  -----------------------------
--R             d x + c      - d x - c
--R          c f        + b f          + a
--R                                                    Type: Expression(Integer)
--E 442
--S 443 of 578
r0085:= -2*arctanh((a+2*c*f^(c+d*x))/(a^2-4*b*c)^(1/2))/_
        (a^2-4*b*c)^(1/2)/d/log(f)
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh

--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 443
--S 444 of 578
a0085:= integrate(t0085,x)
--R
--R
--R   (390)
--R   [
--R       log
--R                  +-----------+
--R                2 |          2    (d x + c)log(f) 2
--R              2c \|- 4b c + a  (%e               )
--R            +
--R                    +-----------+
--R                    |          2        2     2    (d x + c)log(f)
--R              (2a c\|- 4b c + a   + 8b c  - 2a c)%e
--R            +
--R                            +-----------+
--R                         2  |          2              3
--R              (- 2b c + a )\|- 4b c + a   + 4a b c - a
--R         /
--R                 (d x + c)log(f) 2       (d x + c)log(f)
--R            c (%e               )  + a %e                + b
--R    /
--R                +-----------+
--R                |          2
--R       d log(f)\|- 4b c + a
--R     ,
--R             +---------+                      +---------+
--R             |        2   (d x + c)log(f)     |        2
--R          2c\|4b c - a  %e                + a\|4b c - a
--R    2atan(-----------------------------------------------)
--R                                     2
--R                             4b c - a
--R    ------------------------------------------------------]
--R                              +---------+
--R                              |        2
--R                     d log(f)\|4b c - a
--R                                   Type: Union(List(Expression(Integer)),...)
--E 444

--S 445 of 578
m0085a:= a0085.1-r0085
--R
--R
--R   (391)
--R       log
--R                  +-----------+
--R                2 |          2    (d x + c)log(f) 2
--R              2c \|- 4b c + a  (%e               )
--R            +
--R                    +-----------+
--R                    |          2        2     2    (d x + c)log(f)
--R              (2a c\|- 4b c + a   + 8b c  - 2a c)%e
--R            +
--R                            +-----------+
--R                         2  |          2              3
--R              (- 2b c + a )\|- 4b c + a   + 4a b c - a
--R         /
--R                 (d x + c)log(f) 2       (d x + c)log(f)
--R            c (%e               )  + a %e                + b
--R     +
--R                        +-----------+
--R                        |          2
--R       - d r0085 log(f)\|- 4b c + a
--R  /
--R              +-----------+
--R              |          2
--R     d log(f)\|- 4b c + a
--R                                                    Type: Expression(Integer)
--E 445
--S 446 of 578
d0085a:= D(m0085a,x)
--R
--R
--R                            (d x + c)log(f)
--R                          %e
--R   (392)  ------------------------------------------------
--R               (d x + c)log(f) 2       (d x + c)log(f)
--R          c (%e               )  + a %e                + b
--R                                                    Type: Expression(Integer)
--E 446
--S 447 of 578
m0085b:= a0085.2-r0085
--R
--R
--R   (393)
--R                +---------+                      +---------+
--R                |        2   (d x + c)log(f)     |        2

--R             2c\|4b c - a  %e                + a\|4b c - a
--R       2atan(-----------------------------------------------)
--R                                        2
--R                                4b c - a
--R     +
--R                        +---------+
--R                        |        2
--R       - d r0085 log(f)\|4b c - a
--R  /
--R              +---------+
--R              |        2
--R     d log(f)\|4b c - a
--R                                                    Type: Expression(Integer)
--E 447
--S 448 of 578
d0085b:= D(m0085b,x)
--R
--R
--R                            (d x + c)log(f)
--R                          %e
--R   (394)  ------------------------------------------------
--R               (d x + c)log(f) 2       (d x + c)log(f)
--R          c (%e               )  + a %e                + b
--R                                                    Type: Expression(Integer)
--E 448
--S 449 of 578
t0086:= x/(a+b*f^(-c-d*x)+c*f^(c+d*x))
--R
--R
--R                        x
--R   (395)  -----------------------------
--R             d x + c      - d x - c
--R          c f        + b f          + a
--R                                                    Type: Expression(Integer)
--E 449
--S 450 of 578
r0086:= (x*log(-(a-(a^2-4*b*c)^(1/2)+2*c*f^(c+d*x))/_
        (-a+(a^2-4*b*c)^(1/2)))*d*log(f)-x*log((a+(a^2-4*b*c)^(1/2)+_
        2*c*f^(c+d*x))/(a+(a^2-4*b*c)^(1/2)))*d*log(f)+_
        polylog(2,2*c*f^(c+d*x)/(-a+(a^2-4*b*c)^(1/2)))-_
        polylog(2,-2*c*f^(c+d*x)/(a+(a^2-4*b*c)^(1/2))))/_
        (a^2-4*b*c)^(1/2)/d^2/log(f)^2
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its

--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 450
--S 451 of 578
a0086:= integrate(t0086,x)
--R
--R
--R             x
--R           ++                 %A
--R   (396)   |   ------------------------------- d%A
--R          ++      %A d + c      - %A d - c
--R               c f         + b f           + a
--R                                         Type: Union(Expression(Integer),...)
--E 451
--S 452 of 578
m0086:= a0086-r0086
--R
--R
--R             x
--R           ++                 %A
--R   (397)   |   ------------------------------- d%A  - r0086
--R          ++      %A d + c      - %A d - c
--R               c f         + b f           + a
--R                                                    Type: Expression(Integer)
--E 452
--S 453 of 578
d0086:= D(m0086,x)
--R
--R
--R                        x
--R   (398)  -----------------------------
--R             d x + c      - d x - c
--R          c f        + b f          + a
--R                                                    Type: Expression(Integer)
--E 453
--S 454 of 578
t0087:= x^2/(a+b*f^(-c-d*x)+c*f^(c+d*x))
--R
--R

--R                         2
--R                        x
--R   (399)  -----------------------------
--R             d x + c      - d x - c
--R          c f        + b f          + a
--R                                                    Type: Expression(Integer)
--E 454
--S 455 of 578
r0087:= (x^2*log(-(a-(a^2-4*b*c)^(1/2)+2*c*f^(c+d*x))/_
        (-a+(a^2-4*b*c)^(1/2)))*d^2*log(f)^2-_
        x^2*log((a+(a^2-4*b*c)^(1/2)+2*c*f^(c+d*x))/_
        (a+(a^2-4*b*c)^(1/2)))*d^2*log(f)^2+_
        2*x*polylog(2,2*c*f^(c+d*x)/(-a+(a^2-4*b*c)^(1/2)))*d*log(f)-_
        2*x*polylog(2,-2*c*f^(c+d*x)/(a+(a^2-4*b*c)^(1/2)))*d*log(f)-_
        2*polylog(3,2*c*f^(c+d*x)/(-a+(a^2-4*b*c)^(1/2)))+_
        2*polylog(3,-2*c*f^(c+d*x)/(a+(a^2-4*b*c)^(1/2))))/_
        (a^2-4*b*c)^(1/2)/d^3/log(f)^3
--R
--R   There are no library operations named polylog
--R      Use HyperDoc Browse or issue
--R                              )what op polylog
--R      to learn if there is any operation containing " polylog " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      polylog with argument type(s)
--R                               PositiveInteger
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 455
--S 456 of 578
a0087:= integrate(t0087,x)
--R
--R
--R             x                 2
--R           ++                %A
--R   (400)   |   ------------------------------- d%A
--R          ++      %A d + c      - %A d - c
--R               c f         + b f           + a
--R                                         Type: Union(Expression(Integer),...)
--E 456
--S 457 of 578
m0087:= a0087-r0087
--R
--R

--R             x                 2
--R           ++                %A
--R   (401)   |   ------------------------------- d%A  - r0087
--R          ++      %A d + c      - %A d - c
--R               c f         + b f           + a
--R                                                    Type: Expression(Integer)
--E 457
--S 458 of 578
d0087:= D(m0087,x)
--R
--R
--R                         2
--R                        x
--R   (402)  -----------------------------
--R             d x + c      - d x - c
--R          c f        + b f          + a
--R                                                    Type: Expression(Integer)
--E 458
--S 459 of 578
t0088:= f^(a+b*x+c*x^2)*g^(d+e*x+f*x^2)
--R
--R
--R              2              2
--R           c x  + b x + a f x  + e x + d
--R   (403)  f              g
--R                                                    Type: Expression(Integer)
--E 459
--S 460 of 578
r0088:= 1/2*f^a*g^d*%pi^(1/2)*erfi(1/2*(b*log(f)+e*log(g)+_
        2*x*c*log(f)+2*x*f*log(g))/(c*log(f)+f*log(g))^(1/2))/(c*log(f)+_
        f*log(g))^(1/2)*exp(-1/4*(b*log(f)+e*log(g))^2/(c*log(f)+f*log(g)))
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 460
--S 461 of 578

a0088:= integrate(t0088,x)
--R
--R
--R             x    2               2
--R           ++   %A c + %A b + a %A f + %A e + d
--R   (404)   |   f               g               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 461
--S 462 of 578
m0088:= a0088-r0088
--R
--R
--R             x    2               2
--R           ++   %A c + %A b + a %A f + %A e + d
--R   (405)   |   f               g               d%A  - r0088
--R          ++
--R                                                    Type: Expression(Integer)
--E 462
--S 463 of 578
d0088:= D(m0088,x)
--R
--R
--R              2              2
--R           c x  + b x + a f x  + e x + d
--R   (406)  f              g
--R                                                    Type: Expression(Integer)
--E 463
--S 464 of 578
t0089:= exp(x)*sin(a+b*x+c*x^2)
--R
--R
--R            x       2
--R   (407)  %e sin(c x  + b x + a)
--R                                                    Type: Expression(Integer)
--E 464
--S 465 of 578
r0089:= 1/4*(-1)^(3/4)*exp(1)^(%i*a+1/4*%i*(1+%i*b)^2/c)*%pi^(1/2)*_
        erf(1/2*(-1)^(1/4)*(1+%i*b+2*%i*c*x)/c^(1/2))/c^(1/2)+_
        1/4*(-1)^(3/4)*exp(1)^(-%i*a-1/4*%i*(1-%i*b)^2/c)*%pi^(1/2)*_
        erfi(1/2*(-1)^(1/4)*(1-%i*b-2*%i*c*x)/c^(1/2))/c^(1/2)
--R
--R   There are 37 exposed and 23 unexposed library operations named *
--R      having 2 argument(s) but none was determined to be applicable.
--R      Use HyperDoc Browse, or issue
--R                                )display op *

--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--R   Cannot find a definition or applicable library operation named *
--R      with argument type(s)
--R                               AlgebraicNumber
--R                        Polynomial(Complex(Integer))
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 465
--S 466 of 578
a0089:= integrate(t0089,x)
--R
--R
--R             x
--R           ++    %A      2
--R   (408)   |   %e  sin(%A c + %A b + a)d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 466
--S 467 of 578
m0089:= a0089-r0089
--R
--R
--R             x
--R           ++    %A      2
--R   (409)   |   %e  sin(%A c + %A b + a)d%A  - r0089
--R          ++
--R                                                    Type: Expression(Integer)
--E 467
--S 468 of 578
d0089:= D(m0089,x)
--R
--R
--R            x       2
--R   (410)  %e sin(c x  + b x + a)
--R                                                    Type: Expression(Integer)
--E 468
--S 469 of 578
t0090:= exp(x)*cos(a+b*x+c*x^2)
--R
--R
--R                 2             x
--R   (411)  cos(c x  + b x + a)%e

--S 470 of 578
r0090:= (-1/8-1/8*%i)*2^(1/2)*%pi^(1/2)*(exp(1/4*%i*(4*a*c+1+2*%i*b-b^2)/c)*_
        erf((1/4+1/4*%i)*2^(1/2)*(1+%i*b+2*%i*c*x)/c^(1/2))+_
        %i*exp(1/4*%i*(-4*a*c-1+2*%i*b+b^2)/c)*_
        erf(1/4*2^(1/2)*(%i*b+2*%i*c*x-1+%i+b+2*c*x)/c^(1/2)))/c^(1/2)
--R
--R   There are 37 exposed and 23 unexposed library operations named *
--R      having 2 argument(s) but none was determined to be applicable.
--R      Use HyperDoc Browse, or issue
--R                                )display op *
--R      to learn more about the available operations. Perhaps
--R      package-calling the operation or using coercions on the arguments
--R      will allow you to apply the operation.
--R
--R   Cannot find a definition or applicable library operation named *
--R      with argument type(s)
--R                               AlgebraicNumber
--R                        Polynomial(Complex(Integer))
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 470
--S 471 of 578
a0090:= integrate(t0090,x)
--R
--R
--R             x
--R           ++        2               %A
--R   (412)   |   cos(%A c + %A b + a)%e  d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 471
--S 472 of 578
m0090:= a0090-r0090
--R
--R
--R             x
--R           ++        2               %A
--R   (413)   |   cos(%A c + %A b + a)%e  d%A  - r0090
--R          ++
--R                                                    Type: Expression(Integer)
--E 472
--S 473 of 578
d0090:= D(m0090,x)

--R
--R
--R                 2             x
--R   (414)  cos(c x  + b x + a)%e
--R                                                    Type: Expression(Integer)
--E 473
--S 474 of 578
t0091:= f^(a+b*x+c*x^2)*sin(c+d*x+e*x^2)
--R
--R
--R                                 2
--R                 2            c x  + b x + a
--R   (415)  sin(e x  + d x + c)f
--R                                                    Type: Expression(Integer)
--E 474
--S 475 of 578
r0091:= 1/4*%i*exp(1)^(-%i*c+(%i*d-b*log(f))^2/(4*%i*e-4*c*log(f)))*f^a*_
        %pi^(1/2)*erf(1/2*(%i*d-b*log(f)+2*x*(%i*e-c*log(f)))/_
        (%i*e-c*log(f))^(1/2))/(%i*e-c*log(f))^(1/2)-_
        1/4*%i*exp(1)^(%i*c-(%i*d+b*log(f))^2/(4*%i*e+4*c*log(f)))*f^a*_
        %pi^(1/2)*erfi(1/2*(%i*d+b*log(f)+2*x*(%i*e+c*log(f)))/_
        (%i*e+c*log(f))^(1/2))/(%i*e+c*log(f))^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                        Expression(Complex(Integer))
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 475
--S 476 of 578
a0091:= integrate(t0091,x)
--R
--R
--R             x                        2
--R           ++        2              %A c + %A b + a
--R   (416)   |   sin(%A e + %A d + c)f               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 476

--S 477 of 578
m0091:= a0091-r0091
--R
--R
--R             x                        2
--R           ++        2              %A c + %A b + a
--R   (417)   |   sin(%A e + %A d + c)f               d%A  - r0091
--R          ++
--R                                                    Type: Expression(Integer)
--E 477
--S 478 of 578
d0091:= D(m0091,x)
--R
--R
--R                                 2
--R                 2            c x  + b x + a
--R   (418)  sin(e x  + d x + c)f
--R                                                    Type: Expression(Integer)
--E 478
--S 479 of 578
t0092:= f^(a+b*x+c*x^2)*cos(c+d*x+e*x^2)
--R
--R
--R                                 2
--R                 2            c x  + b x + a
--R   (419)  cos(e x  + d x + c)f
--R                                                    Type: Expression(Integer)
--E 479
--S 480 of 578
r0092:= 1/4*exp(1)^(-%i*c+(%i*d-b*log(f))^2/(4*%i*e-4*c*log(f)))*f^a*_
        %pi^(1/2)*erf(1/2*(%i*d-b*log(f)+2*x*(%i*e-c*log(f)))/_
        (%i*e-c*log(f))^(1/2))/(%i*e-c*log(f))^(1/2)+_
        1/4*exp(1)^(%i*c-(%i*d+b*log(f))^2/(4*%i*e+4*c*log(f)))*f^a*_
        %pi^(1/2)*erfi(1/2*(%i*d+b*log(f)+2*x*(%i*e+c*log(f)))/_
        (%i*e+c*log(f))^(1/2))/(%i*e+c*log(f))^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                        Expression(Complex(Integer))
--R
--R      Perhaps you should use "@" to indicate the required return type,

--R      or "$" to specify which version of the function you need.
--E 480
--S 481 of 578
a0092:= integrate(t0092,x)
--R
--R
--R             x                        2
--R           ++        2              %A c + %A b + a
--R   (420)   |   cos(%A e + %A d + c)f               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 481
--S 482 of 578
m0092:= a0092-r0092
--R
--R
--R             x                        2
--R           ++        2              %A c + %A b + a
--R   (421)   |   cos(%A e + %A d + c)f               d%A  - r0092
--R          ++
--R                                                    Type: Expression(Integer)
--E 482
--S 483 of 578
d0092:= D(m0092,x)
--R
--R
--R                                 2
--R                 2            c x  + b x + a
--R   (422)  cos(e x  + d x + c)f
--R                                                    Type: Expression(Integer)
--E 483
--S 484 of 578
t0093:= exp(1)^(2*x)*cos(exp(x))
--R
--R
--R            2x      x
--R   (423)  %e  cos(%e )
--R                                                    Type: Expression(Integer)
--E 484
--S 485 of 578
r0093:= cos(exp(x))+exp(x)*sin(exp(x))
--R
--R
--R            x      x          x
--R   (424)  %e sin(%e ) + cos(%e )

--S 486 of 578
a0093:= integrate(t0093,x)
--R
--R
--R            x      x          x
--R   (425)  %e sin(%e ) + cos(%e )
--R                                         Type: Union(Expression(Integer),...)
--E 486
--S 487 of 578
m0093:= a0093-r0093
--R
--R
--R   (426)  0
--R                                                    Type: Expression(Integer)
--E 487
--S 488 of 578
d0093:= D(m0093,x)
--R
--R
--R   (427)  0
--R                                                    Type: Expression(Integer)
--E 488
--S 489 of 578
t0094:= exp(x)*sec(exp(x))
--R
--R
--R            x      x
--R   (428)  %e sec(%e )
--R                                                    Type: Expression(Integer)
--E 489
--S 490 of 578
r0094:= arctanh(sin(exp(x)))
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R

--S 491 of 578
a0094:= integrate(t0094,x)
--R
--R
--R                    x                   x
--R          log(sin(%e ) + 1) - log(sin(%e ) - 1)
--R   (429)  -------------------------------------
--R                            2
--R                                         Type: Union(Expression(Integer),...)
--E 491
--S 492 of 578
m0094:= a0094-r0094
--R
--R
--R                    x                   x
--R          log(sin(%e ) + 1) - log(sin(%e ) - 1) - 2r0094
--R   (430)  ----------------------------------------------
--R                                 2
--R                                                    Type: Expression(Integer)
--E 492
--S 493 of 578
d0094:= D(m0094,x)
--R
--R
--R               x      x
--R             %e cos(%e )
--R   (431)  - -------------
--R                  x 2
--R            sin(%e )  - 1
--R                                                    Type: Expression(Integer)
--E 493
--S 494 of 578
t0095:= (cos(x)+sin(x))/(exp(1)^(-x)+sin(x))
--R
--R
--R          sin(x) + cos(x)
--R   (432)  ---------------
--R                      - x
--R           sin(x) + %e
--R                                                    Type: Expression(Integer)
--E 494
--S 495 of 578

r0095:= log(1+exp(x)*sin(x))
--R
--R
--R                x
--R   (433)  log(%e sin(x) + 1)
--R                                                    Type: Expression(Integer)
--E 495
--S 496 of 578
a0095:= integrate(t0095,x)
--R
--R
--R                 - x            - x 2         2
--R          log(2%e   sin(x) + (%e   )  - cos(x)  + 1) + 2x
--R   (434)  -----------------------------------------------
--R                                 2
--R                                         Type: Union(Expression(Integer),...)
--E 496
--S 497 of 578
m0095:= a0095-r0095
--R
--R
--R   (435)
--R            x                     - x            - x 2         2
--R   - 2log(%e sin(x) + 1) + log(2%e   sin(x) + (%e   )  - cos(x)  + 1) + 2x
--R   -----------------------------------------------------------------------
--R                                      2
--R                                                    Type: Expression(Integer)
--E 497
--S 498 of 578
d0095:= D(m0095,x)
--R
--R
--R   (436)
--R            - x            x      2
--R       (- %e    + cos(x))%e sin(x)
--R     +
--R              - x 2           - x   x     - x
--R       ((- (%e   )  - cos(x)%e   )%e  + %e    + cos(x))sin(x)
--R     +
--R                   - x 2         3            x           - x         2
--R       (- cos(x)(%e   )  + cos(x)  - cos(x))%e  + cos(x)%e    - cos(x)  + 1
--R  /
--R          - x  x      2        - x 2         2       x      - x
--R       2%e   %e sin(x)  + (((%e   )  - cos(x)  + 1)%e  + 2%e   )sin(x)
--R     +
--R          - x 2         2
--R       (%e   )  - cos(x)  + 1

--S 499 of 578
t0096:= exp(x)*cosh(x)*sinh(x)^2
--R
--R
--R                   x       2
--R   (437)  cosh(x)%e sinh(x)
--R                                                    Type: Expression(Integer)
--E 499
--S 500 of 578
r0096:= -1/16*exp(-2*x)-1/16*exp(2*x)+1/32*exp(4*x)-1/8*x
--R
--R
--R            4x      2x      - 2x
--R          %e   - 2%e   - 2%e     - 4x
--R   (438)  ---------------------------
--R                       32
--R                                                    Type: Expression(Integer)
--E 500
--S 501 of 578
a0096:= integrate(t0096,x)
--R
--R
--R   (439)
--R                 3                  2              2                           3
--R       - 3sinh(x)  + 3cosh(x)sinh(x)  + (- 9cosh(x)  - 4x + 2)sinh(x) + cosh(x)
--R     +
--R       (4x + 2)cosh(x)
--R  /
--R     32sinh(x) - 32cosh(x)
--R                                         Type: Union(Expression(Integer),...)
--E 501
--S 502 of 578
m0096:= a0096-r0096
--R
--R
--R   (440)
--R                 3                  2
--R       - 3sinh(x)  + 3cosh(x)sinh(x)
--R     +
--R            4x      2x      - 2x           2                        4x
--R       (- %e   + 2%e   + 2%e     - 9cosh(x)  + 2)sinh(x) + cosh(x)%e
--R     +
--R                   2x             - 2x          3
--R       - 2cosh(x)%e   - 2cosh(x)%e     + cosh(x)  + 2cosh(x)

--R  /
--R     32sinh(x) - 32cosh(x)
--R                                                    Type: Expression(Integer)
--E 502
--S 503 of 578
d0096:= D(m0096,x)
--R
--R
--R   (441)
--R                        2        4x     2x     - 2x                        4x
--R       - 6cosh(x)sinh(x)  + (- %e   + %e   - %e     + 1)sinh(x) + cosh(x)%e
--R     +
--R                  2x            - 2x           3
--R       - cosh(x)%e   + cosh(x)%e     - 2cosh(x)  + cosh(x)
--R  /
--R     8sinh(x) - 8cosh(x)
--R                                                    Type: Expression(Integer)
--E 503
--S 504 of 578
t0097:= f^(a+b*x+c*x^2)*sinh(c+d*x+e*x^2)
--R
--R
--R                                  2
--R                  2            c x  + b x + a
--R   (442)  sinh(e x  + d x + c)f
--R                                                    Type: Expression(Integer)
--E 504
--S 505 of 578
r0097:= -1/4*exp(1)^(-c+(d-b*log(f))^2/(4*e-4*c*log(f)))*f^a*_
        %pi^(1/2)*erf(1/2*(d-b*log(f)+2*x*(e-c*log(f)))/(e-c*log(f))^(1/2))/_
        (e-c*log(f))^(1/2)+1/4*exp(1)^(c-(d+b*log(f))^2/(4*e+4*c*log(f)))*_
        f^a*%pi^(1/2)*erfi(1/2*(d+b*log(f)+2*x*(e+c*log(f)))/_
        (e+c*log(f))^(1/2))/(e+c*log(f))^(1/2)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 505

--S 506 of 578
a0097:= integrate(t0097,x)
--R
--R
--R             x                         2
--R           ++         2              %A c + %A b + a
--R   (443)   |   sinh(%A e + %A d + c)f               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 506
--S 507 of 578
m0097:= a0097-r0097
--R
--R
--R             x                         2
--R           ++         2              %A c + %A b + a
--R   (444)   |   sinh(%A e + %A d + c)f               d%A  - r0097
--R          ++
--R                                                    Type: Expression(Integer)
--E 507
--S 508 of 578
d0097:= D(m0097,x)
--R
--R
--R                                  2
--R                  2            c x  + b x + a
--R   (445)  sinh(e x  + d x + c)f
--R                                                    Type: Expression(Integer)
--E 508
--S 509 of 578
t0098:= f^(a+b*x+c*x^2)*cosh(c+d*x+e*x^2)
--R
--R
--R                                  2
--R                  2            c x  + b x + a
--R   (446)  cosh(e x  + d x + c)f
--R                                                    Type: Expression(Integer)
--E 509
--S 510 of 578
r0098:= 1/4*exp(1)^(-c+(d-b*log(f))^2/(4*e-4*c*log(f)))*f^a*_
        %pi^(1/2)*erf(1/2*(d-b*log(f)+2*x*(e-c*log(f)))/_
        (e-c*log(f))^(1/2))/(e-c*log(f))^(1/2)+_
        1/4*exp(1)^(c-(d+b*log(f))^2/(4*e+4*c*log(f)))*f^a*_
        %pi^(1/2)*erfi(1/2*(d+b*log(f)+2*x*(e+c*log(f)))/_
        (e+c*log(f))^(1/2))/(e+c*log(f))^(1/2)

--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 510
--S 511 of 578
a0098:= integrate(t0098,x)
--R
--R
--R             x                         2
--R           ++         2              %A c + %A b + a
--R   (447)   |   cosh(%A e + %A d + c)f               d%A
--R          ++
--R                                         Type: Union(Expression(Integer),...)
--E 511
--S 512 of 578
m0098:= a0098-r0098
--R
--R
--R             x                         2
--R           ++         2              %A c + %A b + a
--R   (448)   |   cosh(%A e + %A d + c)f               d%A  - r0098
--R          ++
--R                                                    Type: Expression(Integer)
--E 512
--S 513 of 578
d0098:= D(m0098,x)
--R
--R
--R                                  2
--R                  2            c x  + b x + a
--R   (449)  cosh(e x  + d x + c)f
--R                                                    Type: Expression(Integer)
--E 513
--S 514 of 578
t0099:= 1/exp(x)/(1-exp(1)^(-2*x))^(1/2)
--R

--R
--R                   1
--R   (450)  ------------------
--R              +------------+
--R            x |    - 2x
--R          %e \|- %e     + 1
--R                                                    Type: Expression(Integer)
--E 514
--S 515 of 578
r0099:= -arcsin(exp(-x))
--R
--R   There are no library operations named arcsin
--R      Use HyperDoc Browse or issue
--R                               )what op arcsin
--R      to learn if there is any operation containing " arcsin " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arcsin with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 515
--S 516 of 578
a0099:= integrate(t0099,x)
--R
--R
--R                 +----------+
--R                 |   x 2          x
--R   (451)  2atan(\|(%e )  - 1  - %e )
--R                                         Type: Union(Expression(Integer),...)
--E 516
--S 517 of 578
m0099:= a0099-r0099
--R
--R
--R                 +----------+
--R                 |   x 2          x
--R   (452)  2atan(\|(%e )  - 1  - %e ) - r0099
--R                                                    Type: Expression(Integer)
--E 517
--S 518 of 578
d0099:= D(m0099,x)
--R
--R

--R                1
--R   (453)  -------------
--R           +----------+
--R           |   x 2
--R          \|(%e )  - 1
--R                                                    Type: Expression(Integer)
--E 518
--S 519 of 578
t0100:= exp(x)/(-4+exp(1)^(2*x))
--R
--R
--R               x
--R             %e
--R   (454)  --------
--R            2x
--R          %e   - 4
--R                                                    Type: Expression(Integer)
--E 519
--S 520 of 578
r0100:= -1/2*arctanh(1/2*exp(x))
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 520
--S 521 of 578
a0100:= integrate(t0100,x)
--R
--R
--R                  x              x
--R          - log(%e  + 2) + log(%e  - 2)
--R   (455)  -----------------------------
--R                        4
--R                                         Type: Union(Expression(Integer),...)
--E 521
--S 522 of 578
m0100:= a0100-r0100

--R
--R
--R                  x              x
--R          - log(%e  + 2) + log(%e  - 2) - 4r0100
--R   (456)  --------------------------------------
--R                             4
--R                                                    Type: Expression(Integer)
--E 522
--S 523 of 578
d0100:= D(m0100,x)
--R
--R
--R                x
--R              %e
--R   (457)  ----------
--R             x 2
--R          (%e )  - 4
--R                                                    Type: Expression(Integer)
--E 523
--S 524 of 578
t0101:= (exp(1)^(-2*x)+exp(1)^(2*x))/(-exp(1)^(-2*x)+exp(1)^(2*x))
--R
--R
--R            2x     - 2x
--R          %e   + %e
--R   (458)  -------------
--R            2x     - 2x
--R          %e   - %e
--R                                                    Type: Expression(Integer)
--E 524
--S 525 of 578
r0101:= 1/2*log(-exp(-2*x)+exp(2*x))
--R
--R
--R                2x     - 2x
--R          log(%e   - %e    )
--R   (459)  ------------------
--R                   2
--R                                                    Type: Expression(Integer)
--E 525
--S 526 of 578
a0101:= integrate(t0101,x)
--R
--R
--R                 2x 2
--R          log((%e  )  - 1) - 2x

--R   (460)  ---------------------
--R                    2
--R                                         Type: Union(Expression(Integer),...)
--E 526
--S 527 of 578
m0101:= a0101-r0101
--R
--R
--R                 2x 2              2x     - 2x
--R          log((%e  )  - 1) - log(%e   - %e    ) - 2x
--R   (461)  ------------------------------------------
--R                               2
--R                                                    Type: Expression(Integer)
--E 527
--S 528 of 578
d0101:= D(m0101,x)
--R
--R
--R                       - 2x   2x 2      2x
--R                  - 2%e    (%e  )  + 2%e
--R   (462)  ---------------------------------------
--R             2x 3     - 2x   2x 2     2x     - 2x
--R          (%e  )  - %e    (%e  )  - %e   + %e
--R                                                    Type: Expression(Integer)
--E 528
--S 529 of 578
t0102:= exp(x)/(16-exp(1)^(2*x))
--R
--R
--R                 x
--R               %e
--R   (463)  - ---------
--R              2x
--R            %e   - 16
--R                                                    Type: Expression(Integer)
--E 529
--S 530 of 578
r0102:= 1/4*arctanh(1/4*exp(x))
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named

--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 530
--S 531 of 578
a0102:= integrate(t0102,x)
--R
--R
--R                x              x
--R          log(%e  + 4) - log(%e  - 4)
--R   (464)  ---------------------------
--R                       8
--R                                         Type: Union(Expression(Integer),...)
--E 531
--S 532 of 578
m0102:= a0102-r0102
--R
--R
--R                x              x
--R          log(%e  + 4) - log(%e  - 4) - 8r0102
--R   (465)  ------------------------------------
--R                            8
--R                                                    Type: Expression(Integer)
--E 532
--S 533 of 578
d0102:= D(m0102,x)
--R
--R
--R                  x
--R                %e
--R   (466)  - -----------
--R               x 2
--R            (%e )  - 16
--R                                                    Type: Expression(Integer)
--E 533
--S 534 of 578
t0103:= exp(1)^(4*x)/(16+exp(1)^(8*x))^(1/2)
--R
--R
--R                4x
--R              %e
--R   (467)  ------------
--R           +---------+
--R           |  8x

--R          \|%e   + 16
--R                                                    Type: Expression(Integer)
--E 534
--S 535 of 578
r0103:= 1/4*arcsinh(1/4*exp(4*x))
--R
--R   There are no library operations named arcsinh
--R      Use HyperDoc Browse or issue
--R                              )what op arcsinh
--R      to learn if there is any operation containing " arcsinh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arcsinh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 535
--S 536 of 578
a0103:= integrate(t0103,x)
--R
--R
--R                 +------------+
--R                 |   4x 2           4x
--R            log(\|(%e  )  + 16  - %e  )
--R   (468)  - ---------------------------
--R                         4
--R                                         Type: Union(Expression(Integer),...)
--E 536
--S 537 of 578
m0103:= a0103-r0103
--R
--R
--R                 +------------+
--R                 |   4x 2           4x
--R          - log(\|(%e  )  + 16  - %e  ) - 4r0103
--R   (469)  --------------------------------------
--R                             4
--R                                                    Type: Expression(Integer)
--E 537
--S 538 of 578
d0103:= D(m0103,x)
--R
--R
--R                  4x

--R                %e
--R   (470)  ---------------
--R           +------------+
--R           |   4x 2
--R          \|(%e  )  + 16
--R                                                    Type: Expression(Integer)
--E 538
--S 539 of 578
t0104:= 1/exp(x)/(1+2*exp(x))
--R
--R
--R                1
--R   (471)  -------------
--R              x 2     x
--R          2(%e )  + %e
--R                                                    Type: Expression(Integer)
--E 539
--S 540 of 578
r0104:= -exp(-x)+2*log(2+exp(-x))
--R
--R
--R                 - x          - x
--R   (472)  2log(%e    + 2) - %e
--R                                                    Type: Expression(Integer)
--E 540
--S 541 of 578
a0104:= integrate(t0104,x)
--R
--R
--R             x       x             x
--R          2%e log(2%e  + 1) - 2x %e  - 1
--R   (473)  ------------------------------
--R                          x
--R                        %e
--R                                         Type: Union(Expression(Integer),...)
--E 541
--S 542 of 578
m0104:= a0104-r0104
--R
--R
--R             x       x           x      - x           - x        x
--R          2%e log(2%e  + 1) - 2%e log(%e    + 2) + (%e    - 2x)%e  - 1
--R   (474)  ------------------------------------------------------------
--R                                         x
--R                                       %e
--R                                                    Type: Expression(Integer)

--E 542
--S 543 of 578
d0104:= D(m0104,x)
--R
--R
--R                - x 2   x 2      - x 2  x     - x
--R          - 2(%e   ) (%e )  - (%e   ) %e  + %e    + 2
--R   (475)  -------------------------------------------
--R                  - x        x 2      - x       x
--R              (2%e    + 4)(%e )  + (%e    + 2)%e
--R                                                    Type: Expression(Integer)
--E 543
--S 544 of 578
t0105:= exp(x)*sec(-1+exp(x))^3
--R
--R
--R            x      x     3
--R   (476)  %e sec(%e  - 1)
--R                                                    Type: Expression(Integer)
--E 544
--S 545 of 578
r0105:= 1/2*arctanh(sin(-1+exp(x)))+1/2*sec(-1+exp(x))*tan(-1+exp(x))
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 545
--S 546 of 578
a0105:= integrate(t0105,x)
--R
--R
--R   (477)
--R             x     2          x                   x     2          x
--R       cos(%e  - 1) log(sin(%e  - 1) + 1) - cos(%e  - 1) log(sin(%e  - 1) - 1)
--R     +
--R              x
--R       2sin(%e  - 1)

--R  /
--R            x     2
--R     4cos(%e  - 1)
--R                                         Type: Union(Expression(Integer),...)
--E 546
--S 547 of 578
m0105:= a0105-r0105
--R
--R
--R   (478)
--R             x     2          x                   x     2          x
--R       cos(%e  - 1) log(sin(%e  - 1) + 1) - cos(%e  - 1) log(sin(%e  - 1) - 1)
--R     +
--R              x                     x     2
--R       2sin(%e  - 1) - 4r0105 cos(%e  - 1)
--R  /
--R            x     2
--R     4cos(%e  - 1)
--R                                                    Type: Expression(Integer)
--E 547
--S 548 of 578
d0105:= D(m0105,x)
--R
--R
--R   (479)
--R          x      x     4      x      x     2      x       x     2
--R       2%e sin(%e  - 1)  + (%e cos(%e  - 1)  - 2%e )sin(%e  - 1)
--R     +
--R           x      x     4     x      x     2
--R       - %e cos(%e  - 1)  - %e cos(%e  - 1)
--R  /
--R            x     3      x     2          x     3
--R     2cos(%e  - 1) sin(%e  - 1)  - 2cos(%e  - 1)
--R                                                    Type: Expression(Integer)
--E 548
--S 549 of 578
t0106:= exp(x)/(2+3*exp(x)+exp(1)^(2*x))
--R
--R
--R                  x
--R                %e
--R   (480)  ---------------
--R            2x      x
--R          %e   + 3%e  + 2
--R                                                    Type: Expression(Integer)
--E 549

--S 550 of 578
r0106:= -2*arctanh(3+2*exp(x))
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 550
--S 551 of 578
a0106:= integrate(t0106,x)
--R
--R
--R                  x              x
--R   (481)  - log(%e  + 2) + log(%e  + 1)
--R                                         Type: Union(Expression(Integer),...)
--E 551
--S 552 of 578
m0106:= a0106-r0106
--R
--R
--R                  x              x
--R   (482)  - log(%e  + 2) + log(%e  + 1) - r0106
--R                                                    Type: Expression(Integer)
--E 552
--S 553 of 578
d0106:= D(m0106,x)
--R
--R
--R                   x
--R                 %e
--R   (483)  -----------------
--R             x 2      x
--R          (%e )  + 3%e  + 2
--R                                                    Type: Expression(Integer)
--E 553
--S 554 of 578
t0107:= 2^x/(1+4^x)^(1/2)
--R

--R
--R               x
--R              2
--R   (484)  ---------
--R           +------+
--R           | x
--R          \|4  + 1
--R                                                    Type: Expression(Integer)
--E 554
--S 555 of 578
r0107:= arcsinh(2^x)/log(2)
--R
--R   There are no library operations named arcsinh
--R      Use HyperDoc Browse or issue
--R                              )what op arcsinh
--R      to learn if there is any operation containing " arcsinh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arcsinh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 555
--S 556 of 578
a0107:= integrate(t0107,x)
--R
--R
--R   >> Error detected within library code:
--R   integrate: implementation incomplete (constant residues)
--R
--R   Continuing to read the file...
--R
--E 556
--S 557 of 578
m0107:= a0107-r0107
--R
--R
--R   (485)  - r0107 + a0107
--R                                                    Type: Polynomial(Integer)
--E 557
--S 558 of 578
d0107:= D(m0107,x)
--R
--R

--R   (486)  0
--R                                                    Type: Polynomial(Integer)
--E 558
--S 559 of 578
t0108:= exp(1)^(3*x)/(-1+exp(1)^(2*x))
--R
--R
--R              3x
--R            %e
--R   (487)  --------
--R            2x
--R          %e   - 1
--R                                                    Type: Expression(Integer)
--E 559
--S 560 of 578
r0108:= exp(x)-arctanh(exp(x))
--R
--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 560
--S 561 of 578
a0108:= integrate(t0108,x)
--R
--R
--R                  x              x           x
--R          - log(%e  + 1) + log(%e  - 1) + 2%e
--R   (488)  ------------------------------------
--R                            2
--R                                         Type: Union(Expression(Integer),...)
--E 561
--S 562 of 578
m0108:= a0108-r0108
--R
--R
--R                  x              x           x
--R          - log(%e  + 1) + log(%e  - 1) + 2%e  - 2r0108

--R   (489)  ---------------------------------------------
--R                                2
--R                                                    Type: Expression(Integer)
--E 562
--S 563 of 578
d0108:= D(m0108,x)
--R
--R
--R               x 3
--R            (%e )
--R   (490)  ----------
--R             x 2
--R          (%e )  - 1
--R                                                    Type: Expression(Integer)
--E 563
--S 564 of 578
t0109:= exp((a+x)^2)/x^2-2*a*exp((a+x)^2)/x
--R
--R
--R                         2           2
--R                        x  + 2a x + a
--R          (- 2a x + 1)%e
--R   (491)  ----------------------------
--R                        2
--R                       x
--R                                                    Type: Expression(Integer)
--E 564
--S 565 of 578
r0109:= -exp((a+x)^2)/x+%pi^(1/2)*erfi(a+x)
--R
--R   There are no library operations named erfi
--R      Use HyperDoc Browse or issue
--R                                )what op erfi
--R      to learn if there is any operation containing " erfi " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named erfi
--R      with argument type(s)
--R                             Polynomial(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 565
--S 566 of 578
a0109:= integrate(t0109,x)
--R

--R
--R                               2             2
--R             x                a  + 2%A a + %A
--R           ++  (- 2%A a + 1)%e
--R   (492)   |   ------------------------------- d%A
--R          ++                   2
--R                             %A
--R                                         Type: Union(Expression(Integer),...)
--E 566
--S 567 of 578
m0109:= a0109-r0109
--R
--R
--R                               2             2
--R             x                a  + 2%A a + %A
--R           ++  (- 2%A a + 1)%e
--R   (493)   |   ------------------------------- d%A  - r0109
--R          ++                   2
--R                             %A
--R                                                    Type: Expression(Integer)
--E 567
--S 568 of 578
d0109:= D(m0109,x)
--R
--R
--R                         2           2
--R                        x  + 2a x + a
--R          (- 2a x + 1)%e
--R   (494)  ----------------------------
--R                        2
--R                       x
--R                                                    Type: Expression(Integer)
--E 568
--S 569 of 578
t0110:= 1/(-exp(x)+exp(1)^(3*x))
--R
--R
--R               1
--R   (495)  ----------
--R            3x     x
--R          %e   - %e
--R                                                    Type: Expression(Integer)
--E 569
--S 570 of 578
r0110:= exp(-x)-arctanh(exp(x))
--R

--R   There are no library operations named arctanh
--R      Use HyperDoc Browse or issue
--R                              )what op arctanh
--R      to learn if there is any operation containing " arctanh " in its
--R      name.
--R
--R   Cannot find a definition or applicable library operation named
--R      arctanh with argument type(s)
--R                             Expression(Integer)
--R
--R      Perhaps you should use "@" to indicate the required return type,
--R      or "$" to specify which version of the function you need.
--E 570
--S 571 of 578
a0110:= integrate(t0110,x)
--R
--R
--R              x      x          x      x
--R          - %e log(%e  + 1) + %e log(%e  - 1) + 2
--R   (496)  ---------------------------------------
--R                               x
--R                            2%e
--R                                         Type: Union(Expression(Integer),...)
--E 571
--S 572 of 578
m0110:= a0110-r0110
--R
--R
--R              x      x          x      x                 x
--R          - %e log(%e  + 1) + %e log(%e  - 1) - 2r0110 %e  + 2
--R   (497)  ----------------------------------------------------
--R                                     x
--R                                  2%e
--R                                                    Type: Expression(Integer)
--E 572
--S 573 of 578
d0110:= D(m0110,x)
--R
--R
--R                1
--R   (498)  ------------
--R             x 3     x
--R          (%e )  - %e
--R                                                    Type: Expression(Integer)
--E 573
--S 574 of 578

t0111:= 10^(x^(1/2))/x^(1/2)
--R
--R
--R             +-+
--R            \|x
--R          10
--R   (499)  ------
--R            +-+
--R           \|x
--R                                                    Type: Expression(Integer)
--E 574
--S 575 of 578
r0111:= 2^(1+x^(1/2))*5^(x^(1/2))/log(10)
--R
--R
--R            +-+      +-+
--R           \|x  + 1 \|x
--R          2        5
--R   (500)  --------------
--R              log(10)
--R                                                    Type: Expression(Integer)
--E 575
--S 576 of 578
a0111:= integrate(t0111,x)
--R
--R
--R                     +-+
--R             log(10)\|x
--R          2%e
--R   (501)  --------------
--R              log(10)
--R                                         Type: Union(Expression(Integer),...)
--E 576
--S 577 of 578
m0111:= a0111-r0111
--R
--R
--R              +-+      +-+              +-+
--R             \|x  + 1 \|x       log(10)\|x
--R          - 2        5     + 2%e
--R   (502)  ---------------------------------
--R                       log(10)
--R                                                    Type: Expression(Integer)
--E 577
--S 578 of 578
d0111:= D(m0111,x)

--R
--R
--R                               +-+      +-+                     +-+
--R                              \|x  + 1 \|x              log(10)\|x
--R          (- log(5) - log(2))2        5     + 2log(10)%e
--R   (503)  ---------------------------------------------------------
--R                                          +-+
--R                                 2log(10)\|x
--R                                                    Type: Expression(Integer)
--E 578
)spool

———-

References

[1] Rich, Albert D. “Rule-based Mathematics” www.apmaths.uwo.ca/~arich