$SPAD/src/input richder3t.input

Albert Rich and Timothy Daly December 3, 2016

Abstract

(a+b x)^m (c+d)^n (e+f x)^p

There are 2 derivatives that do not match.

Contents

2

— * —

)set break resume
)sys rm -f richder3t.output
)spool richder3t.output
)set message test on
)set message auto off
)clear all

--S 1 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*sqrt(2+3*x))
--R
--R
--R               2            +------+
--R         (- 25x  - 30x - 9)\|5x + 3
--R   (1)  ----------------------------
--R                 +--------+ +------+
--R        (2x - 1)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 1
--S 2 of 357
--r0:=4451/54*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     320/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/7*(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)+5/7*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)*sqrt(2+3*x)+335/63*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 2
--S 3 of 357
--d0:=t0-D(r0,x)
--E 3
)clear all
--S 4 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))
--R
--R
--R                 2            +------+
--R           (- 25x  - 30x - 9)\|5x + 3
--R   (1)  ---------------------------------
--R           2          +--------+ +------+
--R        (6x  + x - 2)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 4
--S 5 of 357
--r0:=1159/63*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_

--     185/63*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/7*(3+5*x)^(5/2)/(sqrt(1-2*x)*sqrt(2+3*x))+4/49*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/sqrt(2+3*x)+155/147*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 5
--S 6 of 357
--d0:=t0-D(r0,x)
--E 6
)clear all
--S 7 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))
--R
--R
--R                      2            +------+
--R                (- 25x  - 30x - 9)\|5x + 3
--R   (1)  ------------------------------------------
--R            3      2           +--------+ +------+
--R        (18x  + 15x  - 4x - 4)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 7
--S 8 of 357
--r0:=2797/1323*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     2020/1323*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/7*(3+5*x)^(5/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+8/147*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/(2+3*x)^(3/2)+598/3087*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 8
--S 9 of 357
--d0:=t0-D(r0,x)
--E 9
)clear all
--S 10 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2))
--R
--R
--R                          2            +------+
--R                    (- 25x  - 30x - 9)\|5x + 3
--R   (1)  --------------------------------------------------
--R            4      3      2            +--------+ +------+
--R        (54x  + 81x  + 18x  - 20x - 8)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 10
--S 11 of 357
--r0:=-31202/9261*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_

--     81164/9261*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
--     2/7*(3+5*x)^(5/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+12/245*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/(2+3*x)^(5/2)+1514/15435*sqrt(1-2*x)*sqrt(3+5*x)/_
--     (2+3*x)^(3/2)-81164/108045*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 11
--S 12 of 357
--d0:=t0-D(r0,x)
--E 12
)clear all
--S 13 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(9/2))
--R
--R
--R                               2            +------+
--R                         (- 25x  - 30x - 9)\|5x + 3
--R   (1)  -------------------------------------------------------------
--R             5       4       3      2             +--------+ +------+
--R        (162x  + 351x  + 216x  - 24x  - 64x - 16)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 13
--S 14 of 357
--r0:=-213544/151263*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+106558/151263*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/7*(3+5*x)^(5/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+_
--     16/343*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+986/12005*_
--     sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-106772/252105*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)-106558/1764735*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 14
--S 15 of 357
--d0:=t0-D(r0,x)
--E 15
)clear all
--S 16 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(11/2))
--R
--R
--R   (1)
--R                                2            +------+
--R                          (- 25x  - 30x - 9)\|5x + 3
--R   -------------------------------------------------------------------------
--R        6        5        4       3       2              +--------+ +------+
--R   (486x  + 1377x  + 1350x  + 360x  - 240x  - 176x - 32)\|- 2x + 1 \|3x + 2

--R                                                    Type: Expression(Integer)
--E 16
--S 17 of 357
--r0:=-6036028/9529569*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)-3929980/9529569*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/7*(3+5*x)^(5/2)/((2+3*x)^(9/2)*_
--     sqrt(1-2*x))+20/441*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+_
--     4930/64827*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-167228/453789*_
--     sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-392998/3176523*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)+6036028/22235661*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 17
--S 18 of 357
--d0:=t0-D(r0,x)
--E 18
)clear all
--S 19 of 357
t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*sqrt(3+5*x))
--R
--R
--R              3      2            +------+
--R        (- 27x  - 54x  - 36x - 8)\|3x + 2
--R   (1)  ----------------------------------
--R                    +--------+ +------+
--R           (2x - 1)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 19
--S 20 of 357
--r0:=-11291/2750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_
--     168123/2750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+2/11*(2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)+_
--     312/275*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+3/11*(2+3*x)^(5/2)*_
--     sqrt(1-2*x)*sqrt(3+5*x)+14517/2750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 20
--S 21 of 357
--d0:=t0-D(r0,x)
--E 21
)clear all
--S 22 of 357
t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*sqrt(3+5*x))
--R
--R

--R              2            +------+
--R         (- 9x  - 12x - 4)\|3x + 2
--R   (1)  ----------------------------
--R                 +--------+ +------+
--R        (2x - 1)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 22
--S 23 of 357
--r0:=1597/110*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     161/55*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/11*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)+3/11*(2+3*x)^(3/2)*_
--     sqrt(1-2*x)*sqrt(3+5*x)+69/55*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 23
--S 24 of 357
--d0:=t0-D(r0,x)
--E 24
)clear all
--S 25 of 357
t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*sqrt(3+5*x))
--R
--R
--R                        +------+
--R             (- 3x - 2)\|3x + 2
--R   (1)  ----------------------------
--R                 +--------+ +------+
--R        (2x - 1)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 25
--S 26 of 357
--r0:=34/11*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     7/11*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/11*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)+3/11*sqrt(1-2*x)*_
--     sqrt(2+3*x)*sqrt(3+5*x)
--E 26
--S 27 of 357
--d0:=t0-D(r0,x)
--E 27
)clear all
--S 28 of 357
t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))
--R
--R

--R                     +------+
--R                    \|3x + 2
--R   (1)  - ----------------------------
--R                   +--------+ +------+
--R          (2x - 1)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 28
--S 29 of 357
--r0:=elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_
--     2/11*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
--E 29
--S 30 of 357
--d0:=t0-D(r0,x)
--E 30
)clear all
--S 31 of 357
t0:=1/((1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x))
--R
--R
--R                            1
--R   (1)  - -------------------------------------
--R                   +--------+ +------+ +------+
--R          (2x - 1)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 31
--S 32 of 357
--r0:=2/11*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(5/7)*_
--     sqrt(-3-5*x)/sqrt(3+5*x)+4/77*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
--E 32
--S 33 of 357
--d0:=t0-D(r0,x)
--E 33
)clear all
--S 34 of 357
t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x))
--R
--R
--R                               1
--R   (1)  - ------------------------------------------
--R             2          +--------+ +------+ +------+
--R          (6x  + x - 2)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)

--E 34
--S 35 of 357
--r0:=-62/77*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     20/77*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     4/77*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+186/539*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 35
--S 36 of 357
--d0:=t0-D(r0,x)
--E 36
)clear all
--S 37 of 357
t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x))
--R
--R
--R                                   1
--R   (1)  - ---------------------------------------------------
--R              3      2           +--------+ +------+ +------+
--R          (18x  + 15x  - 4x - 4)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 37
--S 38 of 357
--r0:=60/539*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_
--     1752/539*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     4/77*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+54/539*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)+5256/3773*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 38
--S 39 of 357
--d0:=t0-D(r0,x)
--E 39
)clear all
--S 40 of 357
t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*sqrt(3+5*x))
--R
--R
--R                                       1
--R   (1)  - -----------------------------------------------------------
--R              4      3      2            +--------+ +------+ +------+
--R          (54x  + 81x  + 18x  - 20x - 8)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 40

--S 41 of 357
--r0:=6872/3773*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     244604/3773*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
--     4/77*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))+138/2695*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(5/2)+10308/18865*sqrt(1-2*x)*sqrt(3+5*x)/_
--     (2+3*x)^(3/2)+733812/132055*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 41
--S 42 of 357
--d0:=t0-D(r0,x)
--E 42
)clear all
--S 43 of 357
t0:=(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
--R
--R
--R              4       3       2             +------+
--R        (- 81x  - 216x  - 216x  - 96x - 16)\|3x + 2
--R   (1)  --------------------------------------------
--R                 2          +--------+ +------+
--R             (10x  + x - 3)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 43
--S 44 of 357
--r0:=2911577/75625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-1173529/151250*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(9/2)/(sqrt(1-2*x)*_
--     sqrt(3+5*x))-4/121*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
--     10851/15125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+111/605*_
--     (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+502941/151250*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 44
--S 45 of 357
--d0:=t0-D(r0,x)
--E 45
)clear all
--S 46 of 357
t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
--R
--R
--R              3      2            +------+
--R        (- 27x  - 54x  - 36x - 8)\|3x + 2
--R   (1)  ----------------------------------
--R            2          +--------+ +------+

--R        (10x  + x - 3)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 46
--S 47 of 357
--r0:=55019/6050*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     5572/3025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/11*(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))-4/121*(2+3*x)^(5/2)*_
--     sqrt(1-2*x)/sqrt(3+5*x)+111/605*(2+3*x)^(3/2)*sqrt(1-2*x)*_
--     sqrt(3+5*x)+2388/3025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 47
--S 48 of 357
--d0:=t0-D(r0,x)
--E 48
)clear all
--S 49 of 357
t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
--R
--R
--R                 2            +------+
--R            (- 9x  - 12x - 4)\|3x + 2
--R   (1)  ----------------------------------
--R            2          +--------+ +------+
--R        (10x  + x - 3)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 49
--S 50 of 357
--r0:=1159/605*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     259/605*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/11*(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))-4/121*(2+3*x)^(3/2)*_
--     sqrt(1-2*x)/sqrt(3+5*x)+111/605*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 50
--S 51 of 357
--d0:=t0-D(r0,x)
--E 51
)clear all
--S 52 of 357
t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
--R
--R
--R                           +------+
--R                (- 3x - 2)\|3x + 2
--R   (1)  ----------------------------------

--R            2          +--------+ +------+
--R        (10x  + x - 3)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 52
--S 53 of 357
--r0:=37/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     28/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/11*(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))-_
--     4/121*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 53
--S 54 of 357
--d0:=t0-D(r0,x)
--E 54
)clear all
--S 55 of 357
t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))
--R
--R
--R                        +------+
--R                       \|3x + 2
--R   (1)  - ----------------------------------
--R              2          +--------+ +------+
--R          (10x  + x - 3)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 55
--S 56 of 357
--r0:=-74/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     4/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
--     2/11*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-20/121*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 56
--S 57 of 357
--d0:=t0-D(r0,x)
--E 57
)clear all
--S 58 of 357
t0:=1/((1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x))
--R
--R
--R                               1
--R   (1)  - -------------------------------------------
--R              2          +--------+ +------+ +------+

--R          (10x  + x - 3)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 58
--S 59 of 357
--r0:=74/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     40/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     4/77*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_
--     370/847*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 59
--S 60 of 357
--d0:=t0-D(r0,x)
--E 60
)clear all
--S 61 of 357
t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2))
--R
--R
--R                                   1
--R   (1)  - ---------------------------------------------------
--R              3      2           +--------+ +------+ +------+
--R          (30x  + 23x  - 7x - 6)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 61
--S 62 of 357
--r0:=4636/847*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     740/847*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     4/77/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))+186/539*_
--     sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-23180/5929*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 62
--S 63 of 357
--d0:=t0-D(r0,x)
--E 63
)clear all
--S 64 of 357
t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2))
--R
--R
--R                                        1
--R   (1)  - -------------------------------------------------------------
--R              4       3      2             +--------+ +------+ +------+
--R          (90x  + 129x  + 25x  - 32x - 12)\|- 2x + 1 \|3x + 2 \|5x + 3

--S 65 of 357
--r0:=220076/5929*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     31840/5929*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     4/77/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))+54/539*_
--     sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+9876/3773*sqrt(1-2*x)/_
--     (sqrt(2+3*x)*sqrt(3+5*x))-1100380/41503*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 65
--S 66 of 357
--d0:=t0-D(r0,x)
--E 66
)clear all
--S 67 of 357
t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*(3+5*x)^(3/2))
--R
--R
--R   (1)
--R                                        1
--R   - -----------------------------------------------------------------------
--R          5       4       3      2              +--------+ +------+ +------+
--R     (270x  + 567x  + 333x  - 46x  - 100x - 24)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 67
--S 68 of 357
--r0:=-1341176/41503*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+46585232/41503*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+4/77/((2+3*x)^(5/2)*sqrt(1-2*x)*_
--     sqrt(3+5*x))+138/2695*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_
--     14928/18865*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
--     2101332/132055*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
--     46585232/290521*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 68
--S 69 of 357
--d0:=t0-D(r0,x)
--E 69
)clear all
--S 70 of 357
t0:=(2+3*x)^(11/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
--R
--R

--R               5       4        3       2              +------+
--R        (- 243x  - 810x  - 1080x  - 720x  - 240x - 32)\|3x + 2
--R   (1)  -------------------------------------------------------
--R                  3      2            +--------+ +------+
--R              (50x  + 35x  - 12x - 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 70
--S 71 of 357
--r0:=604915631/24956250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-121995881/24956250*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(11/2)/((3+5*x)^(3/2)*_
--     sqrt(1-2*x))-8/363*(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
--     1022/19965*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
--     380188/831875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     4553/33275*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     17427983/8318750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 71
--S 72 of 357
--d0:=t0-D(r0,x)
--E 72
)clear all
--S 73 of 357
t0:=(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
--R
--R
--R              4       3       2             +------+
--R        (- 81x  - 216x  - 216x  - 96x - 16)\|3x + 2
--R   (1)  --------------------------------------------
--R             3      2            +--------+ +------+
--R         (50x  + 35x  - 12x - 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 73
--S 74 of 357
--r0:=5684677/998250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-581651/499125*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(9/2)/((3+5*x)^(3/2)*_
--     sqrt(1-2*x))-8/363*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
--     178/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+4421/33275*_
--     (2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+83093/166375*sqrt(1-2*x)*_
--     sqrt(2+3*x)*sqrt(3+5*x)
--E 74
--S 75 of 357
--d0:=t0-D(r0,x)
--E 75

)clear all
--S 76 of 357
t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
--R
--R
--R                   3      2            +------+
--R             (- 27x  - 54x  - 36x - 8)\|3x + 2
--R   (1)  -------------------------------------------
--R            3      2            +--------+ +------+
--R        (50x  + 35x  - 12x - 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 76
--S 77 of 357
--r0:=118898/99825*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-30023/99825*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(7/2)/((3+5*x)^(3/2)*_
--     sqrt(1-2*x))-8/363*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
--     758/19965*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+4289/33275*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 77
--S 78 of 357
--d0:=t0-D(r0,x)
--E 78
)clear all
--S 79 of 357
t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
--R
--R
--R                      2            +------+
--R                 (- 9x  - 12x - 4)\|3x + 2
--R   (1)  -------------------------------------------
--R            3      2            +--------+ +------+
--R        (50x  + 35x  - 12x - 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 79
--S 80 of 357
--r0:=4157/19965*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     4382/19965*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/11*(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-8/363*(2+3*x)^(3/2)*_
--     sqrt(1-2*x)/(3+5*x)^(3/2)-626/19965*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 80
--S 81 of 357

--d0:=t0-D(r0,x)
--E 81
)clear all
--S 82 of 357
t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
--R
--R
--R                               +------+
--R                    (- 3x - 2)\|3x + 2
--R   (1)  -------------------------------------------
--R            3      2            +--------+ +------+
--R        (50x  + 35x  - 12x - 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 82
--S 83 of 357
--r0:=494/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     1610/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/11*(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-8/363*sqrt(1-2*x)*_
--     sqrt(2+3*x)/(3+5*x)^(3/2)-494/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 83
--S 84 of 357
--d0:=t0-D(r0,x)
--E 84
)clear all
--S 85 of 357
t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(5/2))
--R
--R
--R                            +------+
--R                           \|3x + 2
--R   (1)  - -------------------------------------------
--R              3      2            +--------+ +------+
--R          (50x  + 35x  - 12x - 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 85
--S 86 of 357
--r0:=-724/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     98/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
--     2/11*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-40/363*sqrt(1-2*x)*_
--     sqrt(2+3*x)/(3+5*x)^(3/2)-490/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 86
--S 87 of 357

)clear all
--S 88 of 357
t0:=1/((1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x))
--R
--R
--R                                    1
--R   (1)  - ----------------------------------------------------
--R              3      2            +--------+ +------+ +------+
--R          (50x  + 35x  - 12x - 9)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 88
--S 89 of 357
--r0:=-3896/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     340/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     4/77*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-410/2541*sqrt(1-2*x)*_
--     sqrt(2+3*x)/(3+5*x)^(3/2)+19480/27951*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 89
--S 90 of 357
--d0:=t0-D(r0,x)
--E 90
)clear all
--S 91 of 357
t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2))
--R
--R
--R                                         1
--R   (1)  - --------------------------------------------------------------
--R               4       3      2             +--------+ +------+ +------+
--R          (150x  + 205x  + 34x  - 51x - 18)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 91
--S 92 of 357
--r0:=-595324/27951*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)+85160/27951*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+4/77/((3+5*x)^(3/2)*sqrt(1-2*x)*_
--     sqrt(2+3*x))+186/539*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
--     45040/17787*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
--     2976620/195657*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 92

--S 93 of 357
--d0:=t0-D(r0,x)
--E 93
)clear all
--S 94 of 357
t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2))
--R
--R
--R   (1)
--R                                        1
--R   - -----------------------------------------------------------------------
--R          5       4       3      2              +--------+ +------+ +------+
--R     (450x  + 915x  + 512x  - 85x  - 156x - 36)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 94
--S 95 of 357
--r0:=-42623864/195657*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)+6132760/195657*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+4/77/((2+3*x)^(3/2)*(3+5*x)^(3/2)*_
--     sqrt(1-2*x))+54/539*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
--     14496/3773*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
--     3205940/124509*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
--     213119320/1369599*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 95
--S 96 of 357
--d0:=t0-D(r0,x)
--E 96
)clear all
--S 97 of 357
t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*(3+5*x)^(5/2))
--R
--R
--R   (1)
--R   -
--R        1
--R     /
--R                6        5        4       3       2              +--------+
--R          (1350x  + 3645x  + 3366x  + 769x  - 638x  - 420x - 72)\|- 2x + 1
--R       *
--R           +------+ +------+
--R          \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 97

--S 98 of 357
--r0:=347423024/1369599*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-12071114168/1369599*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+4/77/((2+3*x)^(5/2)*(3+5*x)^(3/2)*_
--     sqrt(1-2*x))+138/2695*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_
--     19548/18865*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
--     4115652/132055*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
--     181551856/871563*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
--     12071114168/9587193*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 98
--S 99 of 357
--d0:=t0-D(r0,x)
--E 99
)clear all
--S 100 of 357
t0:=(2+3*x)^(9/2)*sqrt(3+5*x)/(1-2*x)^(5/2)
--R
--R
--R            4       3       2             +------+ +------+
--R        (81x  + 216x  + 216x  + 96x + 16)\|3x + 2 \|5x + 3
--R   (1)  ---------------------------------------------------
--R                        2           +--------+
--R                     (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 100
--S 101 of 357
--r0:=6478333/16500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     112543103/8250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+1/3*(2+3*x)^(9/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-166/33*_
--     (2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)-139163/3850*(2+3*x)^(3/2)*_
--     sqrt(1-2*x)*sqrt(3+5*x)-1327/154*(2+3*x)^(5/2)*sqrt(1-2*x)*_
--     sqrt(3+5*x)-6478333/38500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 101
--S 102 of 357
--d0:=t0-D(r0,x)
--E 102
)clear all
--S 103 of 357
t0:=(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(5/2)
--R
--R
--R            3      2            +------+ +------+
--R        (27x  + 54x  + 36x + 8)\|3x + 2 \|5x + 3

--R   (1)  -----------------------------------------
--R                   2           +--------+
--R                (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 103
--S 104 of 357
--r0:=-1289089/3300*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+129857/1650*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+1/3*(2+3*x)^(7/2)*sqrt(3+5*x)/_
--     (1-2*x)^(3/2)-133/33*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)-_
--     797/110*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-18551/550*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 104
--S 105 of 357
--d0:=t0-D(r0,x)
--E 105
)clear all
--S 106 of 357
t0:=(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(5/2)
--R
--R
--R           2            +------+ +------+
--R        (9x  + 12x + 4)\|3x + 2 \|5x + 3
--R   (1)  ---------------------------------
--R               2           +--------+
--R            (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 106
--S 107 of 357
--r0:=-4621/66*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
--     931/66*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     1/3*(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-100/33*(2+3*x)^(3/2)*_
--     sqrt(3+5*x)/sqrt(1-2*x)-133/22*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 107
--S 108 of 357
--d0:=t0-D(r0,x)
--E 108
)clear all
--S 109 of 357
t0:=(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(5/2)
--R
--R

--R                 +------+ +------+
--R        (3x + 2)\|3x + 2 \|5x + 3
--R   (1)  --------------------------
--R            2           +--------+
--R         (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 109
--S 110 of 357
--r0:=67/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     133/66*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
--     1/3*(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-67/33*sqrt(2+3*x)*_
--     sqrt(3+5*x)/sqrt(1-2*x)
--E 110
--S 111 of 357
--d0:=t0-D(r0,x)
--E 111
)clear all
--S 112 of 357
t0:=sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(5/2)
--R
--R
--R             +------+ +------+
--R            \|3x + 2 \|5x + 3
--R   (1)  -------------------------
--R           2           +--------+
--R        (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 112
--S 113 of 357
--r0:=-34/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     5/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     1/3*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)-68/231*sqrt(2+3*x)*_
--     sqrt(3+5*x)/sqrt(1-2*x)
--E 113
--S 114 of 357
--d0:=t0-D(r0,x)
--E 114
)clear all
--S 115 of 357
t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*sqrt(2+3*x))
--R
--R

--R                      +------+
--R                     \|5x + 3
--R   (1)  ----------------------------------
--R           2           +--------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 115
--S 116 of 357
--r0:=31/231*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     10/231*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/21*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+62/1617*sqrt(2+3*x)*_
--     sqrt(3+5*x)/sqrt(1-2*x)
--E 116
--S 117 of 357
--d0:=t0-D(r0,x)
--E 117
)clear all
--S 118 of 357
t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(3/2))
--R
--R
--R                         +------+
--R                        \|5x + 3
--R   (1)  -----------------------------------------
--R            3     2           +--------+ +------+
--R        (12x  - 4x  - 5x + 2)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 118
--S 119 of 357
--r0:=458/1617*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     970/1617*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))+194/1617*sqrt(3+5*x)/_
--     (sqrt(1-2*x)*sqrt(2+3*x))-458/3773*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 119
--S 120 of 357
--d0:=t0-D(r0,x)
--E 120
)clear all
--S 121 of 357
t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(5/2))
--R
--R

--R                             +------+
--R                            \|5x + 3
--R   (1)  -------------------------------------------------
--R            4      3      2           +--------+ +------+
--R        (36x  + 12x  - 23x  - 4x + 4)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 121
--S 122 of 357
--r0:=-338/11319*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     4580/11319*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+326/1617*sqrt(3+5*x)/_
--     ((2+3*x)^(3/2)*sqrt(1-2*x))-458/3773*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)+338/26411*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 122
--S 123 of 357
--d0:=t0-D(r0,x)
--E 123
)clear all
--S 124 of 357
t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(7/2))
--R
--R
--R                                  +------+
--R                                 \|5x + 3
--R   (1)  ----------------------------------------------------------
--R             5       4      3      2           +--------+ +------+
--R        (108x  + 108x  - 45x  - 58x  + 4x + 8)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 124
--S 125 of 357
--r0:=-10876/79233*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     189368/79233*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
--     2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+458/1617*sqrt(3+5*x)/_
--     ((2+3*x)^(5/2)*sqrt(1-2*x))-2818/18865*sqrt(1-2*x)*sqrt(3+5*x)/_
--     (2+3*x)^(5/2)-5438/132055*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     189368/924385*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 125
--S 126 of 357
--d0:=t0-D(r0,x)
--E 126
)clear all
--S 127 of 357

t0:=(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2)
--R
--R
--R             4       3       2              +------+ +------+
--R        (135x  + 351x  + 342x  + 148x + 24)\|3x + 2 \|5x + 3
--R   (1)  -----------------------------------------------------
--R                         2           +--------+
--R                      (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 127
--S 128 of 357
--r0:=1/3*(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)+188443/300*_
--     elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-6547351/300*_
--     elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-56/11*_
--     (2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x)-1341/154*(2+3*x)^(3/2)*_
--     (3+5*x)^(3/2)*sqrt(1-2*x)-140289/3850*(3+5*x)^(3/2)*sqrt(1-2*x)*_
--     sqrt(2+3*x)-2166399/7700*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 128
--S 129 of 357
--d0:=t0-D(r0,x)
--E 129
)clear all
--S 130 of 357
t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2)
--R
--R
--R            3      2             +------+ +------+
--R        (45x  + 87x  + 56x + 12)\|3x + 2 \|5x + 3
--R   (1)  ------------------------------------------
--R                    2           +--------+
--R                 (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 130
--S 131 of 357
--r0:=1/3*(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)-37663/60*_
--     elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
--     1897/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     45/11*(2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x)-807/110*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)*sqrt(2+3*x)-6231/110*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 131
--S 132 of 357
--d0:=t0-D(r0,x)
--E 132

--S 133 of 357
t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2)
--R
--R
--R            2            +------+ +------+
--R        (15x  + 19x + 6)\|3x + 2 \|5x + 3
--R   (1)  ----------------------------------
--R                2           +--------+
--R             (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 133
--S 134 of 357
--r0:=1/3*(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)+_
--     137/6*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     68/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_
--     34/11*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)-225/22*sqrt(1-2*x)*_
--     sqrt(2+3*x)*sqrt(3+5*x)
--E 134
--S 135 of 357
--d0:=t0-D(r0,x)
--E 135
)clear all
--S 136 of 357
t0:=(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(5/2)
--R
--R
--R                 +------+ +------+
--R        (5x + 3)\|3x + 2 \|5x + 3
--R   (1)  --------------------------
--R            2           +--------+
--R         (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 136
--S 137 of 357
--r0:=-139/6*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     10/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     1/3*(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-23/7*sqrt(2+3*x)*_
--     sqrt(3+5*x)/sqrt(1-2*x)
--E 137
--S 138 of 357
--d0:=t0-D(r0,x)
--E 138

--S 139 of 357
t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*sqrt(2+3*x))
--R
--R
--R                          +------+
--R                 (5x + 3)\|5x + 3
--R   (1)  ----------------------------------
--R           2           +--------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 139
--S 140 of 357
--r0:=-37/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     5/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/21*(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-13/49*sqrt(2+3*x)*_
--     sqrt(3+5*x)/sqrt(1-2*x)
--E 140
--S 141 of 357
--d0:=t0-D(r0,x)
--E 141
)clear all
--S 142 of 357
t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(3/2))
--R
--R
--R                             +------+
--R                    (5x + 3)\|5x + 3
--R   (1)  -----------------------------------------
--R            3     2           +--------+ +------+
--R        (12x  - 4x  - 5x + 2)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 142
--S 143 of 357
--r0:=19/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     40/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*sqrt(2+3*x))+9/49*sqrt(3+5*x)/_
--     (sqrt(1-2*x)*sqrt(2+3*x))-19/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 143
--S 144 of 357
--d0:=t0-D(r0,x)
--E 144

--S 145 of 357
t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(5/2))
--R
--R
--R                                 +------+
--R                        (5x + 3)\|5x + 3
--R   (1)  -------------------------------------------------
--R            4      3      2           +--------+ +------+
--R        (36x  + 12x  - 23x  - 4x + 4)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 145
--S 146 of 357
--r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+_
--     496/1029*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)-890/1029*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+31/49*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-_
--     89/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-496/2401*_
--     sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 146
--S 147 of 357
--d0:=t0-D(r0,x)
--E 147
)clear all
--S 148 of 357
t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(7/2))
--R
--R
--R                                      +------+
--R                             (5x + 3)\|5x + 3
--R   (1)  ----------------------------------------------------------
--R             5       4      3      2           +--------+ +------+
--R        (108x  + 108x  - 45x  - 58x  + 4x + 8)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 148
--S 149 of 357
--r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))-_
--     4528/7203*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     3946/7203*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
--     53/49*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-_
--     779/1715*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-_
--     2264/12005*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-_
--     3946/84035*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)

--E 149
--S 150 of 357
--d0:=t0-D(r0,x)
--E 150
)clear all
--S 151 of 357
t0:=(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2)
--R
--R
--R             5        4        3        2              +------+ +------+
--R        (675x  + 2160x  + 2763x  + 1766x  + 564x + 72)\|3x + 2 \|5x + 3
--R   (1)  ----------------------------------------------------------------
--R                               2           +--------+
--R                            (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 151
--S 152 of 357
--r0:=1/3*(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_
--     2513419/540*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     174654791/1080*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)-203/33*(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x)-_
--     225/22*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-1310203/4620*_
--     (3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-6277/154*(3+5*x)^(5/2)*_
--     sqrt(1-2*x)*sqrt(2+3*x)-1313411/630*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 152
--S 153 of 357
--d0:=t0-D(r0,x)
--E 153
)clear all
--S 154 of 357
t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2)
--R
--R
--R             4       3       2              +------+ +------+
--R        (225x  + 570x  + 541x  + 228x + 36)\|3x + 2 \|5x + 3
--R   (1)  -----------------------------------------------------
--R                         2           +--------+
--R                      (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 154
--S 155 of 357
--r0:=1/3*(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_

--     4019/4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     69819/2*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
--     170/33*(2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x)-_
--     28283/462*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     1355/154*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     12601/28*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 155
--S 156 of 357
--d0:=t0-D(r0,x)
--E 156
)clear all
--S 157 of 357
t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2)
--R
--R
--R            3       2             +------+ +------+
--R        (75x  + 140x  + 87x + 18)\|3x + 2 \|5x + 3
--R   (1)  -------------------------------------------
--R                    2           +--------+
--R                 (4x  - 4x + 1)\|- 2x + 1
--R                                                    Type: Expression(Integer)
--E 157
--S 158 of 357
--r0:=1/3*(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)-_
--     12101/12*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
--     1219/6*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     137/33*(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)-_
--     817/66*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     91*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 158
--S 159 of 357
--d0:=t0-D(r0,x)
--E 159
)clear all
--S 160 of 357
t0:=(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(5/2)
--R
--R
--R            2            +------+ +------+
--R        (25x  + 30x + 9)\|3x + 2 \|5x + 3
--R   (1)  ----------------------------------
--R                2           +--------+
--R             (4x  - 4x + 1)\|- 2x + 1

--S 161 of 357
--r0:=-4621/18*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     665/18*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     1/3*(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-104/21*(3+5*x)^(3/2)*_
--     sqrt(2+3*x)/sqrt(1-2*x)-695/42*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 161
--S 162 of 357
--d0:=t0-D(r0,x)
--E 162
)clear all
--S 163 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*sqrt(2+3*x))
--R
--R
--R                 2            +------+
--R             (25x  + 30x + 9)\|5x + 3
--R   (1)  ----------------------------------
--R           2           +--------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 163
--S 164 of 357
--r0:=-1597/42*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     115/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/21*(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-_
--     109/147*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)-_
--     120/49*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 164
--S 165 of 357
--d0:=t0-D(r0,x)
--E 165
)clear all
--S 166 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(3/2))
--R
--R
--R                    2            +------+
--R                (25x  + 30x + 9)\|5x + 3
--R   (1)  -----------------------------------------
--R            3     2           +--------+ +------+

--R        (12x  - 4x  - 5x + 2)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 166
--S 167 of 357
--r0:=5/49*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_
--     146/49*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*sqrt(2+3*x))-43/147*(3+5*x)^(3/2)/_
--     (sqrt(1-2*x)*sqrt(2+3*x))-17/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 167
--S 168 of 357
--d0:=t0-D(r0,x)
--E 168
)clear all
--S 169 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(5/2))
--R
--R
--R                        2            +------+
--R                    (25x  + 30x + 9)\|5x + 3
--R   (1)  -------------------------------------------------
--R            4      3      2           +--------+ +------+
--R        (36x  + 12x  - 23x  - 4x + 4)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 169
--S 170 of 357
--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+169/3087*_
--     elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     2290/3087*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     23/147*(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+19/1029*_
--     sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-169/7203*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 170
--S 171 of 357
--d0:=t0-D(r0,x)
--E 171
)clear all
--S 172 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(7/2))
--R
--R
--R                             2            +------+
--R                         (25x  + 30x + 9)\|5x + 3

--R   (1)  ----------------------------------------------------------
--R             5       4      3      2           +--------+ +------+
--R        (108x  + 108x  - 45x  - 58x  + 4x + 8)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 172
--S 173 of 357
--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))-_
--     986/2401*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_
--     9206/2401*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
--     89/147*(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+143/1715*_
--     sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-4437/12005*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)-27618/84035*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 173
--S 174 of 357
--d0:=t0-D(r0,x)
--E 174
)clear all
--S 175 of 357
t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(9/2))
--R
--R
--R                                  2            +------+
--R                              (25x  + 30x + 9)\|5x + 3
--R   (1)  ---------------------------------------------------------------------
--R             6       5      4       3       2             +--------+ +------+
--R        (324x  + 540x  + 81x  - 264x  - 104x  + 32x + 16)\|- 2x + 1 \|3x + 2
--R                                                    Type: Expression(Integer)
--E 175
--S 176 of 357
--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2))+_
--     98642/352947*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)-337780/352947*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+155/147*(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+_
--     355/2401*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-_
--     11433/16807*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-_
--     33778/117649*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-_
--     98642/823543*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 176
--S 177 of 357
--d0:=t0-D(r0,x)
--E 177
)clear all

--S 178 of 357
t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*sqrt(3+5*x))
--R
--R
--R            4       3       2             +------+
--R        (81x  + 216x  + 216x  + 96x + 16)\|3x + 2
--R   (1)  ------------------------------------------
--R               2           +--------+ +------+
--R            (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 178
--S 179 of 357
--r0:=-44109377/181500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+2221688/45375*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(9/2)*sqrt(3+5*x)/_
--     (1-2*x)^(3/2)-227/363*(2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)-_
--     27271/6050*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-130/121*_
--     (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-317384/15125*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 179
--S 180 of 357
--d0:=t0-D(r0,x)
--E 180
)clear all
--S 181 of 357
t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*sqrt(3+5*x))
--R
--R
--R             3      2            +------+
--R         (27x  + 54x  + 36x + 8)\|3x + 2
--R   (1)  ----------------------------------
--R           2           +--------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 181
--S 182 of 357
--r0:=-78472/1815*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+31619/3630*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(7/2)*sqrt(3+5*x)/_
--     (1-2*x)^(3/2)-161/363*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)-_
--     97/121*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-4517/1210*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 182

)clear all
--S 184 of 357
t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*sqrt(3+5*x))
--R
--R
--R                2            +------+
--R             (9x  + 12x + 4)\|3x + 2
--R   (1)  ----------------------------------
--R           2           +--------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 184
--S 185 of 357
--r0:=-4451/726*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+448/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+2/33*(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-_
--     95/363*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)-64/121*sqrt(1-2*x)*_
--     sqrt(2+3*x)*sqrt(3+5*x)
--E 185
--S 186 of 357
--d0:=t0-D(r0,x)
--E 186
)clear all
--S 187 of 357
t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*sqrt(3+5*x))
--R
--R
--R                          +------+
--R                 (3x + 2)\|3x + 2
--R   (1)  ----------------------------------
--R           2           +--------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 187
--S 188 of 357
--r0:=29/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     31/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(35)+2/33*(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-_
--     29/363*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
--E 188

)clear all
--S 190 of 357
t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*sqrt(3+5*x))
--R
--R
--R                      +------+
--R                     \|3x + 2
--R   (1)  ----------------------------------
--R           2           +--------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 190
--S 191 of 357
--r0:=37/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     20/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/33*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+74/2541*sqrt(2+3*x)*_
--     sqrt(3+5*x)/sqrt(1-2*x)
--E 191
--S 192 of 357
--d0:=t0-D(r0,x)
--E 192
)clear all
--S 193 of 357
t0:=1/((1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x))
--R
--R
--R                             1
--R   (1)  -------------------------------------------
--R           2           +--------+ +------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 193
--S 194 of 357
--r0:=272/2541*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     1030/2541*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     4/231*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+544/17787*_
--     sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)
--E 194

)clear all
--S 196 of 357
t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x))
--R
--R
--R                                 1
--R   (1)  --------------------------------------------------
--R            3     2           +--------+ +------+ +------+
--R        (12x  - 4x  - 5x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 196
--S 197 of 357
--r0:=-5594/17787*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     4040/17787*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))+808/17787*_
--     sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+5594/41503*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 197
--S 198 of 357
--d0:=t0-D(r0,x)
--E 198
)clear all
--S 199 of 357
t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x))
--R
--R
--R                                     1
--R   (1)  ----------------------------------------------------------
--R            4      3      2           +--------+ +------+ +------+
--R        (36x  + 12x  - 23x  - 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 199
--S 200 of 357
--r0:=-184636/124509*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)+9740/124509*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+_
--     1072/17787*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+_
--     974/41503*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     184636/290521*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 200

)clear all
--S 202 of 357
t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*sqrt(3+5*x))
--R
--R
--R                                         1
--R   (1)  -------------------------------------------------------------------
--R             5       4      3      2           +--------+ +------+ +------+
--R        (108x  + 108x  - 45x  - 58x  + 4x + 8)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 202
--S 203 of 357
--r0:=699808/871563*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     26062156/871563*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+_
--     1336/17787*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-_
--     806/207515*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
--     349904/1452605*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     26062156/10168235*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 203
--S 204 of 357
--d0:=t0-D(r0,x)
--E 204
)clear all
--S 205 of 357
t0:=(2+3*x)^(11/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
--R
--R
--R             5       4        3       2              +------+
--R        (243x  + 810x  + 1080x  + 720x  + 240x + 32)\|3x + 2
--R   (1)  -----------------------------------------------------
--R                  3     2           +--------+ +------+
--R              (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 205
--S 206 of 357
--r0:=-1508889271/9982500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+151997573/4991250*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(11/2)/((1-2*x)^(3/2)*_

--     sqrt(3+5*x))-223/363*(2+3*x)^(9/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_
--     215/3993*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
--     932783/332750*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
--     4439/6655*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
--     21713939/1663750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 206
--S 207 of 357
--d0:=t0-D(r0,x)
--E 207
)clear all
--S 208 of 357
t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
--R
--R
--R            4       3       2             +------+
--R        (81x  + 216x  + 216x  + 96x + 16)\|3x + 2
--R   (1)  ------------------------------------------
--R             3     2           +--------+ +------+
--R         (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 208
--S 209 of 357
--r0:=-5327983/199650*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+1073233/199650*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(9/2)/((1-2*x)^(3/2)*_
--     sqrt(3+5*x))-157/363*(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_
--     149/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
--     3284/6655*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
--     153319/66550*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 209
--S 210 of 357
--d0:=t0-D(r0,x)
--E 210
)clear all
--S 211 of 357
t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
--R
--R
--R                 3      2            +------+
--R             (27x  + 54x  + 36x + 8)\|3x + 2
--R   (1)  -----------------------------------------
--R            3     2           +--------+ +------+
--R        (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3

--S 212 of 357
--r0:=-148831/39930*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+14903/19965*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(7/2)/((1-2*x)^(3/2)*_
--     sqrt(3+5*x))-91/363*(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_
--     83/3993*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
--     2129/6655*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 212
--S 213 of 357
--d0:=t0-D(r0,x)
--E 213
)clear all
--S 214 of 357
t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
--R
--R
--R                    2            +------+
--R                 (9x  + 12x + 4)\|3x + 2
--R   (1)  -----------------------------------------
--R            3     2           +--------+ +------+
--R        (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 214
--S 215 of 357
--r0:=-974/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
--     119/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/33*(2+3*x)^(5/2)/((1-2*x)^(3/2)*sqrt(3+5*x))-_
--     25/363*(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_
--     17/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 215
--S 216 of 357
--d0:=t0-D(r0,x)
--E 216
)clear all
--S 217 of 357
t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
--R
--R
--R                             +------+
--R                    (3x + 2)\|3x + 2

--R   (1)  -----------------------------------------
--R            3     2           +--------+ +------+
--R        (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 217
--S 218 of 357
--r0:=-362/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     49/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
--     2/33*(2+3*x)^(3/2)/((1-2*x)^(3/2)*sqrt(3+5*x))+_
--     41/363*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_
--     245/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 218
--S 219 of 357
--d0:=t0-D(r0,x)
--E 219
)clear all
--S 220 of 357
t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(3/2))
--R
--R
--R                         +------+
--R                        \|3x + 2
--R   (1)  -----------------------------------------
--R            3     2           +--------+ +------+
--R        (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 220
--S 221 of 357
--r0:=494/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     1150/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/33*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+214/2541*sqrt(2+3*x)/_
--     (sqrt(1-2*x)*sqrt(3+5*x))-2470/27951*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 221
--S 222 of 357
--d0:=t0-D(r0,x)
--E 222
)clear all
--S 223 of 357
t0:=1/((1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x))
--R
--R
--R                                 1

--R   (1)  --------------------------------------------------
--R            3     2           +--------+ +------+ +------+
--R        (20x  - 8x  - 7x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 223
--S 224 of 357
--r0:=8314/27951*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_
--     6260/27951*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     4/231*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+_
--     824/17787*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_
--     41570/195657*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 224
--S 225 of 357
--d0:=t0-D(r0,x)
--E 225
)clear all
--S 226 of 357
t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2))
--R
--R
--R                                     1
--R   (1)  ----------------------------------------------------------
--R            4      3      2           +--------+ +------+ +------+
--R        (60x  + 16x  - 37x  - 5x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 226
--S 227 of 357
--r0:=475592/195657*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)-85780/195657*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*sqrt(2+3*x)*_
--     sqrt(3+5*x))+1088/17787/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))+_
--     5314/41503*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
--     2377960/1369599*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 227
--S 228 of 357
--d0:=t0-D(r0,x)
--E 228
)clear all
--S 229 of 357
t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2))
--R
--R

--R                                          1
--R   (1)  --------------------------------------------------------------------
--R             5       4      3      2            +--------+ +------+ +------+
--R        (180x  + 168x  - 79x  - 89x  + 8x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 229
--S 230 of 357
--r0:=22738708/1369599*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)-3323720/1369599*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*(2+3*x)^(3/2)*_
--     sqrt(3+5*x))+1352/17787/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))+_
--     694/41503*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
--     336536/290521*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
--     113693540/9587193*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 230
--S 231 of 357
--d0:=t0-D(r0,x)
--E 231
)clear all
--S 232 of 357
t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*(3+5*x)^(3/2))
--R
--R
--R   (1)
--R     1
--R  /
--R            6       5      4       3       2             +--------+ +------+
--R       (540x  + 864x  + 99x  - 425x  - 154x  + 52x + 24)\|- 2x + 1 \|3x + 2
--R    *
--R        +------+
--R       \|5x + 3
--R                                                    Type: Expression(Integer)
--E 232
--S 233 of 357
--r0:=-139423864/9587193*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+4839325048/9587193*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+4/231/((1-2*x)^(3/2)*(2+3*x)^(5/2)*_
--     sqrt(3+5*x))+1616/17787/((2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x))-_
--     2206/207515*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_
--     499564/1452605*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
--     72709316/10168235*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
--     4839325048/67110351*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 233
--S 234 of 357

)clear all
--S 235 of 357
t0:=(2+3*x)^(13/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
--R
--R
--R             6        5        4        3        2              +------+
--R        (729x  + 2916x  + 4860x  + 4320x  + 2160x  + 576x + 64)\|3x + 2
--R   (1)  ----------------------------------------------------------------
--R                    4      3      2           +--------+ +------+
--R               (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 235
--S 236 of 357
--r0:=2/33*(2+3*x)^(13/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_
--     51601293223/549037500*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)*sqrt(7/5)+2598959587/137259375*_
--     elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     73/121*(2+3*x)^(11/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+_
--     215/3993*(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_
--     6503/219615*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
--     31887029/18301250*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
--     150812/366025*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
--     371279941/45753125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 236
--S 237 of 357
--d0:=t0-D(r0,x)
--E 237
)clear all
--S 238 of 357
t0:=(2+3*x)^(11/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
--R
--R
--R             5       4        3       2              +------+
--R        (243x  + 810x  + 1080x  + 720x  + 240x + 32)\|3x + 2
--R   (1)  -----------------------------------------------------
--R               4      3      2           +--------+ +------+
--R          (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 238
--S 239 of 357
--r0:=2/33*(2+3*x)^(11/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_

--     90397364/5490375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+36399853/10980750*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-51/121*(2+3*x)^(9/2)/((3+5*x)^(3/2)*_
--     sqrt(1-2*x))+149/3993*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_
--     865/43923*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
--     110519/366025*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
--     5199979/3660250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 239
--S 240 of 357
--d0:=t0-D(r0,x)
--E 240
)clear all
--S 241 of 357
t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
--R
--R
--R                4       3       2             +------+
--R            (81x  + 216x  + 216x  + 96x + 16)\|3x + 2
--R   (1)  --------------------------------------------------
--R             4      3      2           +--------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 241
--S 242 of 357
--r0:=2/33*(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_
--     4971289/2196150*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+491582/1098075*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-29/121*(2+3*x)^(7/2)/((3+5*x)^(3/2)*_
--     sqrt(1-2*x))+83/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_
--     2147/219615*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-_
--     70226/366025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 242
--S 243 of 357
--d0:=t0-D(r0,x)
--E 243
)clear all
--S 244 of 357
t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
--R
--R
--R                     3      2            +------+
--R                 (27x  + 54x  + 36x + 8)\|3x + 2
--R   (1)  --------------------------------------------------

--R             4      3      2           +--------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 244
--S 245 of 357
--r0:=2/33*(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_
--     29933/219615*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-217/219615*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-7/121*(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+_
--     17/3993*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-31/219615*_
--     sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 245
--S 246 of 357
--d0:=t0-D(r0,x)
--E 246
)clear all
--S 247 of 357
t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
--R
--R
--R                        2            +------+
--R                     (9x  + 12x + 4)\|3x + 2
--R   (1)  --------------------------------------------------
--R             4      3      2           +--------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 247
--S 248 of 357
--r0:=2/33*(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+_
--     2209/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-4144/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+15/121*(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-_
--     49/3993*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-2209/43923*_
--     sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 248
--S 249 of 357
--d0:=t0-D(r0,x)
--E 249
)clear all
--S 250 of 357
t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
--R

--R
--R                                  +------+
--R                         (3x + 2)\|3x + 2
--R   (1)  --------------------------------------------------
--R             4      3      2           +--------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 250
--S 251 of 357
--r0:=2/33*(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_
--     8774/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+592/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(35)+37/121*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-_
--     575/3993*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-2960/43923*_
--     sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 251
--S 252 of 357
--d0:=t0-D(r0,x)
--E 252
)clear all
--S 253 of 357
t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(5/2))
--R
--R
--R                              +------+
--R                             \|3x + 2
--R   (1)  --------------------------------------------------
--R             4      3      2           +--------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 253
--S 254 of 357
--r0:=4418/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)-5920/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+2/33*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+118/847*_
--     sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-2470/27951*sqrt(1-2*x)*_
--     sqrt(2+3*x)/(3+5*x)^(3/2)-22090/307461*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 254
--S 255 of 357
--d0:=t0-D(r0,x)
--E 255
)clear all

--S 256 of 357
t0:=1/((1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x))
--R
--R
--R                                     1
--R   (1)  -----------------------------------------------------------
--R             4      3      2           +--------+ +------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 256
--S 257 of 357
--r0:=-119732/307461*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)-620/307461*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+4/231*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+_
--     368/5929*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-_
--     18470/195657*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
--     598660/2152227*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 257
--S 258 of 357
--d0:=t0-D(r0,x)
--E 258
)clear all
--S 259 of 357
t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2))
--R
--R
--R   (1)
--R                                      1
--R   -----------------------------------------------------------------------
--R        5       4       3       2             +--------+ +------+ +------+
--R   (300x  + 260x  - 137x  - 136x  + 15x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 259
--S 260 of 357
--r0:=-19885156/2152227*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)+2809040/2152227*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*(3+5*x)^(3/2)*_
--     sqrt(2+3*x))+456/5929/((3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x))+_
--     5034/41503*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
--     1523260/1369599*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
--     99425780/15065589*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 260
--S 261 of 357

)clear all
--S 262 of 357
t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2))
--R
--R
--R   (1)
--R     1
--R  /
--R            6        5       4       3       2             +--------+ +------+
--R       (900x  + 1380x  + 109x  - 682x  - 227x  + 84x + 36)\|- 2x + 1 \|3x + 2
--R    *
--R        +------+
--R       \|5x + 3
--R                                                    Type: Expression(Integer)
--E 262
--S 263 of 357
--r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2))-_
--     1446357824/15065589*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)*sqrt(5/7)+207999160/15065589*_
--     elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     544/5929/((2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x))+_
--     414/41503*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
--     488436/290521*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
--     108842540/9587193*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
--     7231789120/105459123*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 263
--S 264 of 357
--d0:=t0-D(r0,x)
--E 264
)clear all
--S 265 of 357
t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*(3+5*x)^(5/2))
--R
--R
--R   (1)
--R     1
--R  /
--R             7        6        5        4        3       2
--R       (2700x  + 5940x  + 3087x  - 1828x  - 2045x  - 202x  + 276x + 72)
--R    *
--R        +--------+ +------+ +------+
--R       \|- 2x + 1 \|3x + 2 \|5x + 3

--S 266 of 357
--r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2))+_
--     11880958112/105459123*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-412810345784/105459123*_
--     elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
--     632/5929/((2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x))-_
--     3606/207515*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_
--     649224/1452605*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
--     140700876/10168235*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
--     6208896328/67110351*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
--     412810345784/738213861*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 266
--S 267 of 357
--d0:=t0-D(r0,x)
--E 267
)clear all
--S 268 of 357
t0:=(a+b*x)*(A+B*x)*sqrt(c+d*x)/x
--R
--R
--R              2                       +-------+
--R        (B b x  + (A b + B a)x + A a)\|d x + c
--R   (1)  ---------------------------------------
--R                           x
--R                                                    Type: Expression(Integer)
--E 268
--S 269 of 357
r0:=-2/15*(2*b*B*c-5*A*b*d-2*a*B*d)*(c+d*x)^(3/2)/d^2+_
     2/5*B*(a+b*x)*(c+d*x)^(3/2)/d-2*a*A*atanh(sqrt(c+d*x)/sqrt(c))*_
     sqrt(c)+2*a*A*sqrt(c+d*x)
--R
--R
--R   (2)
--R                            +-------+
--R                2 +-+      \|d x + c
--R       - 30A a d \|c atanh(----------)
--R                               +-+
--R                              \|c
--R     +
--R                 2 2                    2                       2
--R           6B b d x  + ((10A b + 10B a)d  + 2B b c d)x + 30A a d
--R         +
--R                                      2

--R           (10A b + 10B a)c d - 4B b c
--R      *
--R          +-------+
--R         \|d x + c
--R  /
--R        2
--R     15d
--R                                                    Type: Expression(Integer)
--E 269
--S 270 of 357
--d0:=t0-D(r0,x)
--E 270
)clear all
--S 271 of 357
t0:=(A+B*x)*(c+d*x)*sqrt(a+b*x)/x
--R
--R
--R              2                       +-------+
--R        (B d x  + (A d + B c)x + A c)\|b x + a
--R   (1)  ---------------------------------------
--R                           x
--R                                                    Type: Expression(Integer)
--E 271
--S 272 of 357
r0:=2/15*(5*b*B*c+2*A*b*d-2*a*B*d)*(a+b*x)^(3/2)/b^2+_
     2/5*d*(a+b*x)^(3/2)*(A+B*x)/b-2*A*c*atanh(sqrt(a+b*x)/sqrt(a))*_
     sqrt(a)+2*A*c*sqrt(a+b*x)
--R
--R
--R   (2)
--R                           +-------+
--R              2  +-+      \|b x + a
--R       - 30A b c\|a atanh(----------)
--R                              +-+
--R                             \|a
--R     +
--R               2   2          2                   2                     2
--R           6B b d x  + ((10A b  + 2B a b)d + 10B b c)x + (10A a b - 4B a )d
--R         +
--R                 2
--R           (30A b  + 10B a b)c
--R      *
--R          +-------+
--R         \|b x + a
--R  /
--R        2

--R     15b
--R                                                    Type: Expression(Integer)
--E 272
--S 273 of 357
d0:=t0-D(r0,x)
--R
--R
--R   (3)  0
--R                                                    Type: Expression(Integer)
--E 273
)clear all
--S 274 of 357
t0:=x^3*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x))
--R
--R
--R                4    3
--R             a x  + x
--R   (1)  ------------------
--R         +---------+ +---+
--R        \|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 274
--S 275 of 357
r0:=-75/128*asin(1-2*a*x)/a^4-75/64*sqrt(a*x-a^2*x^2)/a^4-_
     25/32*x*sqrt(a*x-a^2*x^2)/a^3-5/8*x^2*sqrt(a*x-a^2*x^2)/a^2-_
     1/4*x^3*sqrt(a*x-a^2*x^2)/a
--R
--R
--R                                           +------------+
--R              3 3      2 2                 |   2 2
--R        (- 32a x  - 80a x  - 100a x - 150)\|- a x  + a x  + 75asin(2a x - 1)
--R   (2)  --------------------------------------------------------------------
--R                                            4
--R                                        128a
--R                                                    Type: Expression(Integer)
--E 275
--S 276 of 357
--d0:=t0-D(r0,x)
--E 276
)clear all
--S 277 of 357
t0:=x^2*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x))
--R

--R
--R                3    2
--R             a x  + x
--R   (1)  ------------------
--R         +---------+ +---+
--R        \|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 277
--S 278 of 357
r0:=-11/16*asin(1-2*a*x)/a^3-11/8*sqrt(a*x-a^2*x^2)/a^3-_
     11/12*x*sqrt(a*x-a^2*x^2)/a^2-1/3*x^2*sqrt(a*x-a^2*x^2)/a
--R
--R
--R                                +------------+
--R              2 2               |   2 2
--R        (- 16a x  - 44a x - 66)\|- a x  + a x  + 33asin(2a x - 1)
--R   (2)  ---------------------------------------------------------
--R                                      3
--R                                   48a
--R                                                    Type: Expression(Integer)
--E 278
--S 279 of 357
--d0:=t0-D(r0,x)
--E 279
)clear all
--S 280 of 357
t0:=x*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x))
--R
--R
--R                2
--R             a x  + x
--R   (1)  ------------------
--R         +---------+ +---+
--R        \|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 280
--S 281 of 357
r0:=-7/8*asin(1-2*a*x)/a^2-5/4*sqrt(a*x)*sqrt(1-a*x)/a^2-_
     1/2*(1+a*x)*sqrt(a*x)*sqrt(1-a*x)/a^2
--R
--R
--R                      +---------+ +---+
--R        (- 4a x - 14)\|- a x + 1 \|a x  + 7asin(2a x - 1)
--R   (2)  -------------------------------------------------
--R                                 2

--R                               8a
--R                                                    Type: Expression(Integer)
--E 281
--S 282 of 357
--d0:=t0-D(r0,x)
--E 282
)clear all
--S 283 of 357
t0:=(1+a*x)/(sqrt(a*x)*sqrt(1-a*x))
--R
--R
--R              a x + 1
--R   (1)  ------------------
--R         +---------+ +---+
--R        \|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 283
--S 284 of 357
r0:=-3/2*asin(1-2*a*x)/a-sqrt(a*x)*sqrt(1-a*x)/a
--R
--R
--R            +---------+ +---+
--R        - 2\|- a x + 1 \|a x  + 3asin(2a x - 1)
--R   (2)  ---------------------------------------
--R                           2a
--R                                                    Type: Expression(Integer)
--E 284
--S 285 of 357
--d0:=t0-D(r0,x)
--E 285
)clear all
--S 286 of 357
t0:=(1+a*x)/(x*sqrt(a*x)*sqrt(1-a*x))
--R
--R
--R              a x + 1
--R   (1)  -------------------
--R          +---------+ +---+
--R        x\|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 286
--S 287 of 357

r0:=-asin(1-2*a*x)-2*sqrt(a*x-a^2*x^2)/(a*x)
--R
--R
--R            +------------+
--R            |   2 2
--R        - 2\|- a x  + a x  + a x asin(2a x - 1)
--R   (2)  ---------------------------------------
--R                          a x
--R                                                    Type: Expression(Integer)
--E 287
--S 288 of 357
--d0:=t0-D(r0,x)
--E 288
)clear all
--S 289 of 357
t0:=(1+a*x)/(x^2*sqrt(a*x)*sqrt(1-a*x))
--R
--R
--R               a x + 1
--R   (1)  --------------------
--R         2 +---------+ +---+
--R        x \|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 289
--S 290 of 357
r0:=-2/3*sqrt(a*x-a^2*x^2)/(a*x^2)-10/3*sqrt(a*x-a^2*x^2)/x
--R
--R
--R                      +------------+
--R                      |   2 2
--R        (- 10a x - 2)\|- a x  + a x
--R   (2)  ----------------------------
--R                        2
--R                    3a x
--R                                                    Type: Expression(Integer)
--E 290
--S 291 of 357
--d0:=t0-D(r0,x)
--E 291
)clear all
--S 292 of 357
t0:=(1+a*x)/(x^3*sqrt(a*x)*sqrt(1-a*x))
--R

--R
--R               a x + 1
--R   (1)  --------------------
--R         3 +---------+ +---+
--R        x \|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 292
--S 293 of 357
r0:=-2/5*sqrt(a*x-a^2*x^2)/(a*x^3)-6/5*sqrt(a*x-a^2*x^2)/x^2-_
     12/5*a*sqrt(a*x-a^2*x^2)/x
--R
--R
--R                              +------------+
--R              2 2             |   2 2
--R        (- 12a x  - 6a x - 2)\|- a x  + a x
--R   (2)  ------------------------------------
--R                            3
--R                        5a x
--R                                                    Type: Expression(Integer)
--E 293
--S 294 of 357
--d0:=t0-D(r0,x)
--E 294
)clear all
--S 295 of 357
t0:=(1+a*x)/(x^4*sqrt(a*x)*sqrt(1-a*x))
--R
--R
--R               a x + 1
--R   (1)  --------------------
--R         4 +---------+ +---+
--R        x \|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 295
--S 296 of 357
r0:=-2/7*sqrt(a*x-a^2*x^2)/(a*x^4)-26/35*sqrt(a*x-a^2*x^2)/x^3-_
     104/105*a*sqrt(a*x-a^2*x^2)/x^2-208/105*a^2*sqrt(a*x-a^2*x^2)/x
--R
--R
--R                                           +------------+
--R               3 3       2 2               |   2 2
--R        (- 208a x  - 104a x  - 78a x - 30)\|- a x  + a x
--R   (2)  -------------------------------------------------
--R                                   4
--R                             105a x

--S 297 of 357
d0:=t0-D(r0,x)
--R
--R
--R                                                  +------------+
--R                    +---------+ +---+             |   2 2
--R        (- a x - 1)\|- a x + 1 \|a x  + (a x + 1)\|- a x  + a x
--R   (3)  --------------------------------------------------------
--R                      +------------+
--R                    4 |   2 2        +---------+ +---+
--R                   x \|- a x  + a x \|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 297
)clear all
--S 298 of 357
t0:=(1+a*x)/(x^5*sqrt(a*x)*sqrt(1-a*x))
--R
--R
--R               a x + 1
--R   (1)  --------------------
--R         5 +---------+ +---+
--R        x \|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 298
--S 299 of 357
r0:=-2/9*sqrt(a*x-a^2*x^2)/(a*x^5)-34/63*sqrt(a*x-a^2*x^2)/x^4-_
     68/105*a*sqrt(a*x-a^2*x^2)/x^3-272/315*a^2*sqrt(a*x-a^2*x^2)/x^2-_
     544/315*a^3*sqrt(a*x-a^2*x^2)/x
--R
--R
--R                                                      +------------+
--R               4 4       3 3       2 2                |   2 2
--R        (- 544a x  - 272a x  - 204a x  - 170a x - 70)\|- a x  + a x
--R   (2)  ------------------------------------------------------------
--R                                         5
--R                                   315a x
--R                                                    Type: Expression(Integer)
--E 299
--S 300 of 357
d0:=t0-D(r0,x)
--R
--R
--R                                                  +------------+

--R                    +---------+ +---+             |   2 2
--R        (- a x - 1)\|- a x + 1 \|a x  + (a x + 1)\|- a x  + a x
--R   (3)  --------------------------------------------------------
--R                      +------------+
--R                    5 |   2 2        +---------+ +---+
--R                   x \|- a x  + a x \|- a x + 1 \|a x
--R                                                    Type: Expression(Integer)
--E 300
)clear all
--S 301 of 357
t0:=x^m*(e+f*x)^n/((a+b*x)*(c+d*x))
--R
--R
--R                 m         n
--R                x (f x + e)
--R   (1)  ---------------------------
--R             2
--R        b d x  + (a d + b c)x + a c
--R                                                    Type: Expression(Integer)
--E 301
--S 302 of 357
--r0:=b*x^(1+m)*(e+f*x)^n*_
--     AppellF1(1+m,1,-n,2+m,-b*x/a,-f*x/e)/(a*(b*c-a*d)*(1+m)*_
--     ((e+f*x)/e)^n)-d*x^(1+m)*(e+f*x)^n*_
--     AppellF1(1+m,1,-n,2+m,-d*x/c,-f*x/e)/(c*(b*c-a*d)*(1+m)*_
--     ((e+f*x)/e)^n)
--E 302
--S 303 of 357
--d0:=t0-D(r0,x)
--E 303
)clear all
--S 304 of 357
t0:=x^4*(e+f*x)^n/((a+b*x)*(c+d*x))
--R
--R
--R                 4         n
--R                x (f x + e)
--R   (1)  ---------------------------
--R             2
--R        b d x  + (a d + b c)x + a c
--R                                                    Type: Expression(Integer)
--E 304
--S 305 of 357

--r0:=e^2*(e+f*x)^(1+n)/(b*d*f^3*(1+n))+(b*c+a*d)*e*(e+f*x)^(1+n)/_
--     (b^2*d^2*f^2*(1+n))+(b^2*c^2+a*b*c*d+a^2*d^2)*(e+f*x)^(1+n)/_
--     (b^3*d^3*f*(1+n))-2*e*(e+f*x)^(2+n)/(b*d*f^3*(2+n))-_
--     (b*c+a*d)*(e+f*x)^(2+n)/(b^2*d^2*f^2*(2+n))+(e+f*x)^(3+n)/_
--     (b*d*f^3*(3+n))-a^4*(e+f*x)^(1+n)*_
--     hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_
--     (b^3*(b*c-a*d)*(b*e-a*f)*(1+n))+c^4*(e+f*x)^(1+n)*_
--     hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
--     (d^3*(b*c-a*d)*(d*e-c*f)*(1+n))
--E 305
--S 306 of 357
--d0:=t0-D(r0,x)
--E 306
)clear all
--S 307 of 357
t0:=x^3*(e+f*x)^n/((a+b*x)*(c+d*x))
--R
--R
--R                 3         n
--R                x (f x + e)
--R   (1)  ---------------------------
--R             2
--R        b d x  + (a d + b c)x + a c
--R                                                    Type: Expression(Integer)
--E 307
--S 308 of 357
--r0:=-e*(e+f*x)^(1+n)/(b*d*f^2*(1+n))-(b*c+a*d)*(e+f*x)^(1+n)/_
--     (b^2*d^2*f*(1+n))+(e+f*x)^(2+n)/(b*d*f^2*(2+n))+a^3*(e+f*x)^(1+n)*_
--     hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_
--     (b^2*(b*c-a*d)*(b*e-a*f)*(1+n))-c^3*(e+f*x)^(1+n)*_
--     hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
--     (d^2*(b*c-a*d)*(d*e-c*f)*(1+n))
--E 308
--S 309 of 357
--d0:=t0-D(r0,x)
--E 309
)clear all
--S 310 of 357
t0:=x^2*(e+f*x)^n/((a+b*x)*(c+d*x))
--R
--R
--R                 2         n
--R                x (f x + e)

--R   (1)  ---------------------------
--R             2
--R        b d x  + (a d + b c)x + a c
--R                                                    Type: Expression(Integer)
--E 310
--S 311 of 357
--r0:=(e+f*x)^(1+n)/(b*d*f*(1+n))-a^2*(e+f*x)^(1+n)*_
--     hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_
--     (b*(b*c-a*d)*(b*e-a*f)*(1+n))+c^2*(e+f*x)^(1+n)*_
--     hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
--     (d*(b*c-a*d)*(d*e-c*f)*(1+n))
--E 311
--S 312 of 357
--d0:=t0-D(r0,x)
--E 312
)clear all
--S 313 of 357
t0:=x*(e+f*x)^n/((a+b*x)*(c+d*x))
--R
--R
--R                           n
--R                x (f x + e)
--R   (1)  ---------------------------
--R             2
--R        b d x  + (a d + b c)x + a c
--R                                                    Type: Expression(Integer)
--E 313
--S 314 of 357
--r0:=a*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_
--     ((b*c-a*d)*(b*e-a*f)*(1+n))-c*(e+f*x)^(1+n)*_
--     hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
--     ((b*c-a*d)*(d*e-c*f)*(1+n))
--E 314
--S 315 of 357
--d0:=t0-D(r0,x)
--E 315
)clear all
--S 316 of 357
t0:=(e+f*x)^n/((a+b*x)*(c+d*x))
--R
--R
--R                          n

--R                 (f x + e)
--R   (1)  ---------------------------
--R             2
--R        b d x  + (a d + b c)x + a c
--R                                                    Type: Expression(Integer)
--E 316
--S 317 of 357
--r0:=-b*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/_
--     (b*e-a*f))/((b*c-a*d)*(b*e-a*f)*(1+n))+d*(e+f*x)^(1+n)*_
--     hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
--     ((b*c-a*d)*(d*e-c*f)*(1+n))
--E 317
--S 318 of 357
--d0:=t0-D(r0,x)
--E 318
)clear all
--S 319 of 357
t0:=(e+f*x)^n/(x*(a+b*x)*(c+d*x))
--R
--R
--R                           n
--R                  (f x + e)
--R   (1)  ------------------------------
--R             3               2
--R        b d x  + (a d + b c)x  + a c x
--R                                                    Type: Expression(Integer)
--E 319
--S 320 of 357
--r0:=-(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,(e+f*x)/e)/(a*c*e*(1+n))+_
--     b^2*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_
--     (a*(b*c-a*d)*(b*e-a*f)*(1+n))-d^2*(e+f*x)^(1+n)*_
--     hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_
--     (c*(b*c-a*d)*(d*e-c*f)*(1+n))
--E 320
--S 321 of 357
--d0:=t0-D(r0,x)
--E 321
)clear all
--S 322 of 357
t0:=(e+f*x)^n/(x^2*(a+b*x)*(c+d*x))
--R
--R

--R                            n
--R                   (f x + e)
--R   (1)  -------------------------------
--R             4               3        2
--R        b d x  + (a d + b c)x  + a c x
--R                                                    Type: Expression(Integer)
--E 322
--S 323 of 357
--r0:=-(e+f*x)^(1+n)/(a*c*e*x)+(b*c+a*d)*(e+f*x)^(1+n)*_
--     hypergeometric(1,1+n,2+n,(e+f*x)/e)/(a^2*c^2*e*(1+n))-_
--     f*n*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,(e+f*x)/e)/_
--     (a*c*e^2*(1+n))-b^3*(e+f*x)^(1+n)*hypergeometric(1,1+n,_
--     2+n,b*(e+f*x)/(b*e-a*f))/(a^2*(b*c-a*d)*(b*e-a*f)*(1+n))_
--     +d^3*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,d*(e+f*x)/_
--     (d*e-c*f))/(c^2*(b*c-a*d)*(d*e-c*f)*(1+n))
--E 323
--S 324 of 357
--d0:=t0-D(r0,x)
--E 324
)clear all
--S 325 of 357
t0:=(a+b*x)*(c+d*x)*(e+f*x)*(g+h*x)
--R
--R
--R   (1)
--R              4                                       3
--R     b d f h x  + (((a d + b c)f + b d e)h + b d f g)x
--R   +
--R                                                         2
--R     ((a c f + (a d + b c)e)h + ((a d + b c)f + b d e)g)x
--R   +
--R     (a c e h + (a c f + (a d + b c)e)g)x + a c e g
--R                                                    Type: Polynomial(Integer)
--E 325
--S 326 of 357
r0:=a*c*e*g*x+1/2*(b*c*e*g+a*(d*e*g+c*f*g+c*e*h))*x^2+_
     1/3*(b*(d*e*g+c*f*g+c*e*h)+a*(d*f*g+d*e*h+c*f*h))*x^3+_
     1/4*(a*d*f*h+b*(d*f*g+d*e*h+c*f*h))*x^4+1/5*b*d*f*h*x^5
--R
--R
--R   (2)
--R     1          5      1       1         1           1          4
--R     - b d f h x  + (((- a d + - b c)f + - b d e)h + - b d f g)x
--R     5                 4       4         4           4
--R   +

--R       1          1       1             1       1         1          3
--R     ((- a c f + (- a d + - b c)e)h + ((- a d + - b c)f + - b d e)g)x
--R       3          3       3             3       3         3
--R   +
--R      1            1          1       1          2
--R     (- a c e h + (- a c f + (- a d + - b c)e)g)x  + a c e g x
--R      2            2          2       2
--R                                          Type: Polynomial(Fraction(Integer))
--E 326
--S 327 of 357
d0:=t0-D(r0,x)
--R
--R
--R   (3)  0
--R                                          Type: Polynomial(Fraction(Integer))
--E 327
)clear all
--S 328 of 357
t0:=(a+b*x)*(c+d*x)*(e+f*x)/(g+h*x)
--R
--R
--R               3                          2
--R        b d f x  + ((a d + b c)f + b d e)x  + (a c f + (a d + b c)e)x + a c e
--R   (1)  ---------------------------------------------------------------------
--R                                       h x + g
--R                                          Type: Fraction(Polynomial(Integer))
--E 328
--S 329 of 357
r0:=(b*(d*g-c*h)*(f*g-e*h)-a*h*(d*f*g-d*e*h-c*f*h))*x/h^3+_
     1/2*(a*d*f*h-b*(d*f*g-d*e*h-c*f*h))*x^2/h^2+_
     1/3*b*d*f*x^3/h-(b*g-a*h)*(d*g-c*h)*(f*g-e*h)*log(g+h*x)/h^4
--R
--R
--R   (2)
--R                   3                                   2
--R           6a c e h  + (- 6a c f + (- 6a d - 6b c)e)g h
--R         +
--R                                     2            3
--R           ((6a d + 6b c)f + 6b d e)g h - 6b d f g
--R      *
--R         log(h x + g)
--R     +
--R               3 3                              3             2  2
--R       2b d f h x  + (((3a d + 3b c)f + 3b d e)h  - 3b d f g h )x
--R     +
--R                                     3                                 2

--R           (6a c f + (6a d + 6b c)e)h  + ((- 6a d - 6b c)f - 6b d e)g h
--R         +
--R                   2
--R           6b d f g h
--R      *
--R         x
--R  /
--R       4
--R     6h
--R                                                    Type: Expression(Integer)
--E 329
--S 330 of 357
d0:=t0-D(r0,x)
--R
--R
--R   (3)  0
--R                                                    Type: Expression(Integer)
--E 330
)clear all
--S 331 of 357
t0:=(a+b*x)*(c+d*x)/((e+f*x)*(g+h*x))
--R
--R
--R             2
--R        b d x  + (a d + b c)x + a c
--R   (1)  ---------------------------
--R             2
--R        f h x  + (e h + f g)x + e g
--R                                          Type: Fraction(Polynomial(Integer))
--E 331
--S 332 of 357
r0:=b*d*x/(f*h)+(b*e-a*f)*(d*e-c*f)*log(e+f*x)/(f^2*(f*g-e*h))-_
     (b*g-a*h)*(d*g-c*h)*log(g+h*x)/(h^2*(f*g-e*h))
--R
--R
--R   (2)
--R             2 2                 2           2 2
--R       (a c f h  + (- a d - b c)f g h + b d f g )log(h x + g)
--R     +
--R               2                         2  2
--R       (- a c f  + (a d + b c)e f - b d e )h log(f x + e)
--R     +
--R                 2        2
--R       (b d e f h  - b d f g h)x
--R  /
--R        2 3    3   2

--R     e f h  - f g h
--R                                                    Type: Expression(Integer)
--E 332
--S 333 of 357
d0:=t0-D(r0,x)
--R
--R
--R   (3)  0
--R                                                    Type: Expression(Integer)
--E 333
)clear all
--S 334 of 357
t0:=(a+b*x)/((c+d*x)*(e+f*x)*(g+h*x))
--R
--R
--R                                       b x + a
--R   (1)  ---------------------------------------------------------------------
--R               3                          2
--R        d f h x  + ((c f + d e)h + d f g)x  + (c e h + (c f + d e)g)x + c e g
--R                                          Type: Fraction(Polynomial(Integer))
--E 334
--S 335 of 357
r0:=-(b*c-a*d)*log(c+d*x)/((d*e-c*f)*(d*g-c*h))+_
     (b*e-a*f)*log(e+f*x)/((d*e-c*f)*(f*g-e*h))-_
     (b*g-a*h)*log(g+h*x)/((d*g-c*h)*(f*g-e*h))
--R
--R
--R   (2)
--R       ((a c f - a d e)h + (- b c f + b d e)g)log(h x + g)
--R     +
--R       ((- a c f + b c e)h + (a d f - b d e)g)log(f x + e)
--R     +
--R       ((a d - b c)e h + (- a d + b c)f g)log(d x + c)
--R  /
--R       2           2  2       2 2    2 2             2    2     2
--R     (c e f - c d e )h  + (- c f  + d e )g h + (c d f  - d e f)g
--R                                                    Type: Expression(Integer)
--E 335
--S 336 of 357
--d0:=t0-D(r0,x)
--E 336
)clear all
--S 337 of 357

t0:=1/((a+b*x)*(c+d*x)*(e+f*x)*(g+h*x))
--R
--R
--R   (1)
--R     1
--R  /
--R                4                                       3
--R       b d f h x  + (((a d + b c)f + b d e)h + b d f g)x
--R     +
--R                                                           2
--R       ((a c f + (a d + b c)e)h + ((a d + b c)f + b d e)g)x
--R     +
--R       (a c e h + (a c f + (a d + b c)e)g)x + a c e g
--R                                          Type: Fraction(Polynomial(Integer))
--E 337
--S 338 of 357
r0:=b^2*log(a+b*x)/((b*c-a*d)*(b*e-a*f)*(b*g-a*h))-_
     d^2*log(c+d*x)/((b*c-a*d)*(d*e-c*f)*(d*g-c*h))+_
     f^2*log(e+f*x)/((b*e-a*f)*(d*e-c*f)*(f*g-e*h))-_
     h^2*log(g+h*x)/((b*g-a*h)*(d*g-c*h)*(f*g-e*h))
--R
--R
--R   (2)
--R            2           2  2       2 2    2 2             2    2     2  2
--R         ((a c d - a b c )f  + (- a d  + b c )e f + (a b d  - b c d)e )h
--R      *
--R         log(h x + g)
--R     +
--R              2           2  2 2     2 2    2 2  2              2    2     2 2
--R         ((- a c d + a b c )f h  + (a d  - b c )f g h + (- a b d  + b c d)f g )
--R      *
--R         log(f x + e)
--R     +
--R             2 2           2 2  2       2 2 2    2 2 2
--R           (a d e f - a b d e )h  + (- a d f  + b d e )g h
--R         +
--R                 2 2    2 2     2
--R           (a b d f  - b d e f)g
--R      *
--R         log(d x + c)
--R     +
--R               2 2       2     2  2     2 2 2    2 2 2
--R           (- b c e f + b c d e )h  + (b c f  - b d e )g h
--R         +
--R               2     2    2 2     2
--R           (- b c d f  + b d e f)g
--R      *
--R         log(b x + a)
--R  /

--R               3 2     2   3    2       3   2      2 3  2
--R             (a c d - a b c )e f  + (- a c d  + a b c )e f
--R           +
--R               2     2      2 2   3
--R             (a b c d  - a b c d)e
--R      *
--R          3
--R         h
--R     +
--R            3 2     2   3  3     3 3    3 3  2        2   3    3 2   3    2
--R       ((- a c d + a b c )f  + (a d  - b c )e f + (- a b d  + b c d)e )g h
--R     +
--R          3   2      2 3  3       3 3    3 3    2       2 3    3   2  3  2
--R       ((a c d  - a b c )f  + (- a d  + b c )e f  + (a b d  - b c d )e )g h
--R     +
--R               2     2      2 2   3     2   3    3 2     2
--R           (- a b c d  + a b c d)f  + (a b d  - b c d)e f
--R         +
--R                 2 3    3   2  2
--R           (- a b d  + b c d )e f
--R      *
--R          3
--R         g
--R                                                    Type: Expression(Integer)
--E 338
--S 339 of 357
--d0:=t0-D(r0,x)
--E 339
)clear all
--S 340 of 357
t0:=(a+b*x)^m*(c+d*x)*(e+f*x)*(g+h*x)
--R
--R
--R   (1)
--R             3                          2
--R     (d f h x  + ((c f + d e)h + d f g)x  + (c e h + (c f + d e)g)x + c e g)
--R  *
--R              m
--R     (b x + a)
--R                                                    Type: Expression(Integer)
--E 340
--S 341 of 357
r0:=(b*c-a*d)*(b*e-a*f)*(b*g-a*h)*(a+b*x)^(1+m)/(b^4*(1+m))+_
     (3*a^2*d*f*h+b^2*(d*e*g+c*f*g+c*e*h)-_
     2*a*b*(d*f*g+d*e*h+c*f*h))*(a+b*x)^(2+m)/(b^4*(2+m))-_
     (3*a*d*f*h-b*(d*f*g+d*e*h+c*f*h))*(a+b*x)^(3+m)/(b^4*(3+m))+_

     d*f*h*(a+b*x)^(4+m)/(b^4*(4+m))
--R
--R
--R   (2)
--R               3           2                               m + 4
--R       (d f h m  + 6d f h m  + 11d f h m + 6d f h)(b x + a)
--R     +
--R                                                  3
--R           (((- 3a d + b c)f + b d e)h + b d f g)m
--R         +
--R                                                      2
--R           (((- 21a d + 7b c)f + 7b d e)h + 7b d f g)m
--R         +
--R           (((- 42a d + 14b c)f + 14b d e)h + 14b d f g)m
--R         +
--R           ((- 24a d + 8b c)f + 8b d e)h + 8b d f g
--R      *
--R                  m + 3
--R         (b x + a)
--R     +
--R                   2                            2
--R               ((3a d - 2a b c)f + (- 2a b d + b c)e)h
--R             +
--R                             2       2
--R               ((- 2a b d + b c)f + b d e)g
--R          *
--R              3
--R             m
--R         +
--R                    2                               2
--R               ((24a d - 16a b c)f + (- 16a b d + 8b c)e)h
--R             +
--R                               2        2
--R               ((- 16a b d + 8b c)f + 8b d e)g
--R          *
--R              2
--R             m
--R         +
--R                    2                                2
--R               ((57a d - 38a b c)f + (- 38a b d + 19b c)e)h
--R             +
--R                                2         2
--R               ((- 38a b d + 19b c)f + 19b d e)g
--R          *
--R             m
--R         +
--R                2                                2
--R           ((36a d - 24a b c)f + (- 24a b d + 12b c)e)h
--R         +
--R                            2         2

--R           ((- 24a b d + 12b c)f + 12b d e)g
--R      *
--R                  m + 2
--R         (b x + a)
--R     +
--R                    3     2          2         2
--R               ((- a d + a b c)f + (a b d - a b c)e)h
--R             +
--R                  2         2            2     3
--R               ((a b d - a b c)f + (- a b d + b c)e)g
--R          *
--R              3
--R             m
--R         +
--R                     3      2           2          2
--R               ((- 9a d + 9a b c)f + (9a b d - 9a b c)e)h
--R             +
--R                   2          2             2      3
--R               ((9a b d - 9a b c)f + (- 9a b d + 9b c)e)g
--R          *
--R              2
--R             m
--R         +
--R                      3       2            2           2
--R               ((- 26a d + 26a b c)f + (26a b d - 26a b c)e)h
--R             +
--R                    2           2              2       3
--R               ((26a b d - 26a b c)f + (- 26a b d + 26b c)e)g
--R          *
--R             m
--R         +
--R                  3       2            2           2
--R           ((- 24a d + 24a b c)f + (24a b d - 24a b c)e)h
--R         +
--R                2           2              2       3
--R           ((24a b d - 24a b c)f + (- 24a b d + 24b c)e)g
--R      *
--R                  m + 1
--R         (b x + a)
--R  /
--R      4 4      4 3      4 2      4       4
--R     b m  + 10b m  + 35b m  + 50b m + 24b
--R                                                    Type: Expression(Integer)
--E 341
--S 342 of 357
d0:=normalize(t0-D(r0,x))
--R
--R
--R   (3)  0

)clear all
--S 343 of 357
t0:=(a+b*x)^m*(c+d*x)*(e+f*x)/(g+h*x)
--R
--R
--R              2                               m
--R        (d f x  + (c f + d e)x + c e)(b x + a)
--R   (1)  ---------------------------------------
--R                        h x + g
--R                                                    Type: Expression(Integer)
--E 343
--S 344 of 357
--r0:=(b*d*e*h*(2+m)+f*(b*c*h-d*(a*h+b*g*(2+m))))*(a+b*x)^(1+m)/_
--     (b^2*h^2*(1+m)*(2+m))+f*(a+b*x)^(1+m)*(c+d*x)/(b*h*(2+m))+_
--     (d*g-c*h)*(f*g-e*h)*(a+b*x)^(1+m)*hypergeometric(1,1+m,2+m,_
--     -h*(a+b*x)/(b*g-a*h))/(h^2*(b*g-a*h)*(1+m))
--E 344
--S 345 of 357
--d0:=t0-D(r0,x)
--E 345
)clear all
--S 346 of 357
t0:=(a+b*x)^m*(c+d*x)/((e+f*x)*(g+h*x))
--R
--R
--R                              m
--R            (d x + c)(b x + a)
--R   (1)  ---------------------------
--R             2
--R        f h x  + (e h + f g)x + e g
--R                                                    Type: Expression(Integer)
--E 346
--S 347 of 357
--r0:=-(d*e-c*f)*(a+b*x)^(1+m)*_
--     hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*_
--     (f*g-e*h)*(1+m))+(d*g-c*h)*(a+b*x)^(1+m)*_
--     hypergeometric(1,1+m,2+m,-h*(a+b*x)/(b*g-a*h))/((b*g-a*h)*_
--     (f*g-e*h)*(1+m))
--E 347
--S 348 of 357

)clear all
--S 349 of 357
t0:=(a+b*x)^m/((c+d*x)*(e+f*x)*(g+h*x))
--R
--R
--R                                               m
--R                                      (b x + a)
--R   (1)  ---------------------------------------------------------------------
--R               3                          2
--R        d f h x  + ((c f + d e)h + d f g)x  + (c e h + (c f + d e)g)x + c e g
--R                                                    Type: Expression(Integer)
--E 349
--S 350 of 357
--r0:=d^2*(a+b*x)^(1+m)*hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/_
--     ((b*c-a*d)*(d*e-c*f)*(d*g-c*h)*(1+m))-f^2*(a+b*x)^(1+m)*_
--     hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*_
--     (d*e-c*f)*(f*g-e*h)*(1+m))+h^2*(a+b*x)^(1+m)*_
--     hypergeometric(1,1+m,2+m,-h*(a+b*x)/(b*g-a*h))/((b*g-a*h)*_
--     (d*g-c*h)*(f*g-e*h)*(1+m))
--E 350
--S 351 of 357
--d0:=t0-D(r0,x)
--E 351
)clear all
--S 352 of 357
t0:=x/((1+x)*(2+x)*(3+x))
--R
--R
--R                 x
--R   (1)  ------------------
--R         3     2
--R        x  + 6x  + 11x + 6
--R                                          Type: Fraction(Polynomial(Integer))
--E 352
--S 353 of 357
r0:=-1/2*log(1+x)+2*log(2+x)-3/2*log(3+x)
--R
--R
--R        - 3log(x + 3) + 4log(x + 2) - log(x + 1)
--R   (2)  ----------------------------------------
--R                            2

--S 354 of 357
d0:=t0-D(r0,x)
--R
--R
--R   (3)  0
--R                                                    Type: Expression(Integer)
--E 354
)clear all
--S 355 of 357
t0:=(-x^2+x^3)/((-6+x)*(3+5*x)^3)
--R
--R
--R                       3    2
--R                      x  - x
--R   (1)  -----------------------------------
--R            4       3        2
--R        125x  - 525x  - 1215x  - 783x - 162
--R                                          Type: Fraction(Polynomial(Integer))
--E 355
--S 356 of 357
r0:=(-12/1375)/(3+5*x)^2+201/15125/(3+5*x)+_
     20/3993*log(6-x)+1493/499125*log(3+5*x)
--R
--R
--R   (2)
--R              2
--R       (37325x  + 44790x + 13437)log(5x + 3)
--R     +
--R              2
--R       (62500x  + 75000x + 22500)log(- x + 6) + 33165x + 15543
--R  /
--R              2
--R     12478125x  + 14973750x + 4492125
--R                                                    Type: Expression(Integer)
--E 356
--S 357 of 357
d0:=t0-D(r0,x)
--R
--R
--R   (3)  0
--R                                                    Type: Expression(Integer)
--E 357

)spool )lisp (bye) ———-

73

References^{[1] nothing}

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