$SPAD/src/input rich3r.input

Albert Rich and Timothy Daly

December 3, 2016

Abstract

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

• 100 integrals in this file.

• 100 supplied ”optimal results”.

• 0 matching answers.

• 0 cases where Axiom supplied 2 results.

• 0 cases that Axiom failed to integrate.

• 100 that contain expressions Axiom does not recognize.

Contents

2

— * —

)set break resume
)sys rm -f rich3r.output
)spool rich3r.output
)set message test on
)set message auto off
)clear all
--S 1 of 500
t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))
--R
--R
--R                     +--------+
--R                    \|- 2x + 1
--R   (1)  ----------------------------------
--R            2            +------+ +------+
--R        (15x  + 19x + 6)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 1
--S 2 of 500
--r0:=-4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     4*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
--     2*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-20*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 2
--S 3 of 500
--a0:=integrate(t0,x)
--E 3
--S 4 of 500
--m0:=a0-r0
--E 4
--S 5 of 500
--d0:=D(m0,x)
--E 5
)clear all
--S 6 of 500
t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))
--R
--R
--R                         +--------+
--R                        \|- 2x + 1
--R   (1)  ------------------------------------------

--R            3      2             +------+ +------+
--R        (45x  + 87x  + 56x + 12)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 6
--S 7 of 500
--r0:=556/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)-80/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+2/3*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
--     92/7*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2780/21*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 7
--S 8 of 500
--a0:=integrate(t0,x)
--E 8
--S 9 of 500
--m0:=a0-r0
--E 9
--S 10 of 500
--d0:=D(m0,x)
--E 10
)clear all
--S 11 of 500
t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*(3+5*x)^(3/2))
--R
--R
--R                              +--------+
--R                             \|- 2x + 1
--R   (1)  -----------------------------------------------------
--R             4       3       2              +------+ +------+
--R        (135x  + 351x  + 342x  + 148x + 24)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 11
--S 12 of 500
--r0:=-3352/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     116464/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/5*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_
--     416/105*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
--     19268/245*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_
--     116464/147*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 12
--S 13 of 500
--a0:=integrate(t0,x)

--E 13
--S 14 of 500
--m0:=a0-r0
--E 14
--S 15 of 500
--d0:=D(m0,x)
--E 15
)clear all
--S 16 of 500
t0:=(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(5/2)
--R
--R
--R            4       3       2             +--------+ +------+
--R        (81x  + 216x  + 216x  + 96x + 16)\|- 2x + 1 \|3x + 2
--R   (1)  -----------------------------------------------------
--R                          2            +------+
--R                      (25x  + 30x + 9)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 16
--S 17 of 500
--r0:=12601/103125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-1473539/206250*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)-2/15*(2+3*x)^(9/2)*sqrt(1-2*x)/_
--     (3+5*x)^(3/2)-118/165*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
--     5153/48125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     958/1925*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
--     12601/240625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 17
--S 18 of 500
--a0:=integrate(t0,x)
--E 18
--S 19 of 500
--m0:=a0-r0
--E 19
--S 20 of 500
--d0:=D(m0,x)
--E 20
)clear all
--S 21 of 500
t0:=(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(5/2)

--R
--R
--R            3      2            +--------+ +------+
--R        (27x  + 54x  + 36x + 8)\|- 2x + 1 \|3x + 2
--R   (1)  -------------------------------------------
--R                     2            +------+
--R                 (25x  + 30x + 9)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 21
--S 22 of 500
--r0:=-47342/103125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-19033/103125*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-2/15*(2+3*x)^(7/2)*sqrt(1-2*x)/_
--     (3+5*x)^(3/2)-458/825*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
--     2818/6875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     2719/34375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 22
--S 23 of 500
--a0:=integrate(t0,x)
--E 23
--S 24 of 500
--m0:=a0-r0
--E 24
--S 25 of 500
--d0:=D(m0,x)
--E 25
)clear all
--S 26 of 500
t0:=(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(5/2)
--R
--R
--R           2            +--------+ +------+
--R        (9x  + 12x + 4)\|- 2x + 1 \|3x + 2
--R   (1)  -----------------------------------
--R                 2            +------+
--R             (25x  + 30x + 9)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 26
--S 27 of 500
--r0:=-169/4125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     3206/4125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     2/15*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
--     326/825*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_

--     458/1375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 27
--S 28 of 500
--a0:=integrate(t0,x)
--E 28
--S 29 of 500
--m0:=a0-r0
--E 29
--S 30 of 500
--d0:=D(m0,x)
--E 30
)clear all
--S 31 of 500
t0:=(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(5/2)
--R
--R
--R                 +--------+ +------+
--R        (3x + 2)\|- 2x + 1 \|3x + 2
--R   (1)  ----------------------------
--R              2            +------+
--R          (25x  + 30x + 9)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 31
--S 32 of 500
--r0:=458/825*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     1358/825*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-2/15*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_
--     194/825*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 32
--S 33 of 500
--a0:=integrate(t0,x)
--E 33
--S 34 of 500
--m0:=a0-r0
--E 34
--S 35 of 500
--d0:=D(m0,x)
--E 35
)clear all

--S 36 of 500
t0:=sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(5/2)
--R
--R
--R            +--------+ +------+
--R           \|- 2x + 1 \|3x + 2
--R   (1)  -------------------------
--R            2            +------+
--R        (25x  + 30x + 9)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 36
--S 37 of 500
--r0:=62/165*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
--     28/165*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-2/15*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-_
--     62/165*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 37
--S 38 of 500
--a0:=integrate(t0,x)
--E 38
--S 39 of 500
--m0:=a0-r0
--E 39
--S 40 of 500
--d0:=D(m0,x)
--E 40
)clear all
--S 41 of 500
t0:=sqrt(1-2*x)/((3+5*x)^(5/2)*sqrt(2+3*x))
--R
--R
--R                     +--------+
--R                    \|- 2x + 1
--R   (1)  ----------------------------------
--R            2            +------+ +------+
--R        (25x  + 30x + 9)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 41
--S 42 of 500
--r0:=-136/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+28/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-2/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
--     136/33*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)

--E 42
--S 43 of 500
--a0:=integrate(t0,x)
--E 43
--S 44 of 500
--m0:=a0-r0
--E 44
--S 45 of 500
--d0:=D(m0,x)
--E 45
)clear all
--S 46 of 500
t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(5/2))
--R
--R
--R                         +--------+
--R                        \|- 2x + 1
--R   (1)  -------------------------------------------
--R            3       2             +------+ +------+
--R        (75x  + 140x  + 87x + 18)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 46
--S 47 of 500
--r0:=536/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     532/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
--     2*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-40/3*sqrt(1-2*x)*_
--     sqrt(2+3*x)/(3+5*x)^(3/2)+2660/33*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 47
--S 48 of 500
--a0:=integrate(t0,x)
--E 48
--S 49 of 500
--m0:=a0-r0
--E 49
--S 50 of 500
--d0:=D(m0,x)
--E 50
)clear all
--S 51 of 500

t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(5/2))
--R
--R
--R                              +--------+
--R                             \|- 2x + 1
--R   (1)  -----------------------------------------------------
--R             4       3       2              +------+ +------+
--R        (225x  + 570x  + 541x  + 228x + 36)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 51
--S 52 of 500
--r0:=-36968/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     5320/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2/3*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+416/21*_
--     sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-2780/21*sqrt(1-2*x)*_
--     sqrt(2+3*x)/(3+5*x)^(3/2)+184840/231*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 52
--S 53 of 500
--a0:=integrate(t0,x)
--E 53
--S 54 of 500
--m0:=a0-r0
--E 54
--S 55 of 500
--d0:=D(m0,x)
--E 55
)clear all
--S 56 of 500
t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*(3+5*x)^(5/2))
--R
--R
--R                                    +--------+
--R                                   \|- 2x + 1
--R   (1)  ----------------------------------------------------------------
--R             5        4        3        2              +------+ +------+
--R        (675x  + 2160x  + 2763x  + 1766x  + 564x + 72)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 56
--S 57 of 500
--r0:=296816/231*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-10312712/231*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/5*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_
--     556/105*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_

--     116044/735*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
--     155104/147*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
--     10312712/1617*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 57
--S 58 of 500
--a0:=integrate(t0,x)
--E 58
--S 59 of 500
--m0:=a0-r0
--E 59
--S 60 of 500
--d0:=D(m0,x)
--E 60
)clear all
--S 61 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)
--R
--R
--R              3      2           +--------+ +------+ +------+
--R   (1)  (- 18x  - 15x  + 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 61
--S 62 of 500
--r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+17427983/16706250*_
--     elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     604915631/16706250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+1103/259875*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+_
--     178/7425*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_
--     124891/2165625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     18177329/38981250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 62
--S 63 of 500
--a0:=integrate(t0,x)
--E 63
--S 64 of 500
--m0:=a0-r0
--E 64
--S 65 of 500
--d0:=D(m0,x)
--E 65

)clear all
--S 66 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)
--R
--R
--R             2          +--------+ +------+ +------+
--R   (1)  (- 6x  - x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 66
--S 67 of 500
--r0:=2/45*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)+83093/151875*_
--     elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     5684677/303750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+62/1575*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_
--     347/39375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     84134/354375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 67
--S 68 of 500
--a0:=integrate(t0,x)
--E 68
--S 69 of 500
--m0:=a0-r0
--E 69
--S 70 of 500
--d0:=D(m0,x)
--E 70
)clear all
--S 71 of 500
t0:=(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)
--R
--R
--R                   +--------+ +------+ +------+
--R   (1)  (- 2x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 71
--S 72 of 500
--r0:=4289/10125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     118898/10125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/35*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_
--     194/2625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     2657/23625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 72

--S 73 of 500
--a0:=integrate(t0,x)
--E 73
--S 74 of 500
--m0:=a0-r0
--E 74
--S 75 of 500
--d0:=D(m0,x)
--E 75
)clear all
--S 76 of 500
t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)
--R
--R
--R                   +--------+ +------+
--R        (- 2x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------
--R                    +------+
--R                   \|3x + 2
--R                                                    Type: Expression(Integer)
--E 76
--S 77 of 500
--r0:=-4157/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+4382/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+2/15*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+214/675*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 77
--S 78 of 500
--a0:=integrate(t0,x)
--E 78
--S 79 of 500
--m0:=a0-r0
--E 79
--S 80 of 500
--d0:=D(m0,x)
--E 80
)clear all
--S 81 of 500
t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)

--R
--R
--R                   +--------+ +------+
--R        (- 2x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------
--R                        +------+
--R               (3x + 2)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 81
--S 82 of 500
--r0:=494/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     1610/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)-16/27*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 82
--S 83 of 500
--a0:=integrate(t0,x)
--E 83
--S 84 of 500
--m0:=a0-r0
--E 84
--S 85 of 500
--d0:=D(m0,x)
--E 85
)clear all
--S 86 of 500
t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)
--R
--R
--R                   +--------+ +------+
--R        (- 2x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------
--R              2            +------+
--R           (9x  + 12x + 4)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 86
--S 87 of 500
--r0:=724/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     98/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_
--     2/9*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+82/27*_
--     sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 87

--S 89 of 500
--m0:=a0-r0
--E 89
--S 90 of 500
--d0:=D(m0,x)
--E 90
)clear all
--S 91 of 500
t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)
--R
--R
--R                    +--------+ +------+
--R         (- 2x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  --------------------------------
--R            3      2            +------+
--R        (27x  + 54x  + 36x + 8)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 91
--S 92 of 500
--r0:=68/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     3896/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)-2/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
--     82/135*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+3896/945*_
--     sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 92
--S 93 of 500
--a0:=integrate(t0,x)
--E 93
--S 94 of 500
--m0:=a0-r0
--E 94
--S 95 of 500
--d0:=D(m0,x)
--E 95
)clear all
--S 96 of 500
t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)

--R
--R
--R                         +--------+ +------+
--R              (- 2x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------------------
--R            4       3       2             +------+
--R        (81x  + 216x  + 216x  + 96x + 16)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 96
--S 97 of 500
--r0:=17032/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-595324/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)-2/21*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
--     82/315*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+8516/6615*_
--     sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+595324/46305*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 97
--S 98 of 500
--a0:=integrate(t0,x)
--E 98
--S 99 of 500
--m0:=a0-r0
--E 99
--S 100 of 500
--d0:=D(m0,x)
--E 100
)clear all
--S 101 of 500
t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(11/2)
--R
--R
--R                               +--------+ +------+
--R                    (- 2x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  -----------------------------------------------------
--R             5       4        3       2              +------+
--R        (243x  + 810x  + 1080x  + 720x  + 240x + 32)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 101
--S 102 of 500
--r0:=1226552/83349*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-42623864/83349*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)-2/27*(1-2*x)^(3/2)*_
--     sqrt(3+5*x)/(2+3*x)^(9/2)+82/567*sqrt(1-2*x)*sqrt(3+5*x)/_

--     (2+3*x)^(7/2)+13136/19845*sqrt(1-2*x)*sqrt(3+5*x)/_
--     (2+3*x)^(5/2)+613276/138915*sqrt(1-2*x)*sqrt(3+5*x)/_
--     (2+3*x)^(3/2)+42623864/972405*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 102
--S 103 of 500
--a0:=integrate(t0,x)
--E 103
--S 104 of 500
--m0:=a0-r0
--E 104
--S 105 of 500
--d0:=D(m0,x)
--E 105
)clear all
--S 106 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)
--R
--R
--R              4       3      2             +--------+ +------+ +------+
--R   (1)  (- 90x  - 129x  - 25x  + 32x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 106
--S 107 of 500
--r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)+_
--     371279941/108590625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-51601293223/434362500*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+601/160875*(2+3*x)^(3/2)*_
--     (3+5*x)^(5/2)*sqrt(1-2*x)+178/10725*(2+3*x)^(5/2)*(3+5*x)^(5/2)*_
--     sqrt(1-2*x)-11725073/56306250*(3+5*x)^(3/2)*sqrt(1-2*x)*_
--     sqrt(2+3*x)-18034/625625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     776112041/506756250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 107
--S 108 of 500
--a0:=integrate(t0,x)
--E 108
--S 109 of 500
--m0:=a0-r0
--E 109
--S 110 of 500
--d0:=D(m0,x)
--E 110

--S 111 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)
--R
--R
--R              3      2           +--------+ +------+ +------+
--R   (1)  (- 30x  - 23x  + 7x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 111
--S 112 of 500
--r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+5199979/3341250*_
--     elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     90397364/1670625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+62/2475*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_
--     40703/433125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     23/9625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     5442127/7796250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 112
--S 113 of 500
--a0:=integrate(t0,x)
--E 113
--S 114 of 500
--m0:=a0-r0
--E 114
--S 115 of 500
--d0:=D(m0,x)
--E 115
)clear all
--S 116 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)
--R
--R
--R              2          +--------+ +------+ +------+
--R   (1)  (- 10x  - x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 116
--S 117 of 500
--r0:=70226/91125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     4971289/182250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/45*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_
--     839/23625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_

--     194/4725*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     76163/212625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 117
--S 118 of 500
--a0:=integrate(t0,x)
--E 118
--S 119 of 500
--m0:=a0-r0
--E 119
--S 120 of 500
--d0:=D(m0,x)
--E 120
)clear all
--S 121 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)
--R
--R
--R              2          +--------+ +------+
--R        (- 10x  - x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------------
--R                       +------+
--R                      \|3x + 2
--R                                                    Type: Expression(Integer)
--E 121
--S 122 of 500
--r0:=-31/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     29933/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_
--     74/525*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1847/4725*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 122
--S 123 of 500
--a0:=integrate(t0,x)
--E 123
--S 124 of 500
--m0:=a0-r0
--E 124
--S 125 of 500
--d0:=D(m0,x)
--E 125

--S 126 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)
--R
--R
--R              2          +--------+ +------+
--R        (- 10x  - x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------------
--R                           +------+
--R                  (3x + 2)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 126
--S 127 of 500
--r0:=-2209/405*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+4144/405*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-2/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)-_
--     8/15*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+494/135*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 127
--S 128 of 500
--a0:=integrate(t0,x)
--E 128
--S 129 of 500
--m0:=a0-r0
--E 129
--S 130 of 500
--d0:=D(m0,x)
--E 130
)clear all
--S 131 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)
--R
--R
--R              2          +--------+ +------+
--R        (- 10x  - x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------------
--R                 2            +------+
--R              (9x  + 12x + 4)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 131
--S 132 of 500
--r0:=-2/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)-_

--     8774/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     592/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(35)+74/9*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-_
--     1150/81*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 132
--S 133 of 500
--a0:=integrate(t0,x)
--E 133
--S 134 of 500
--m0:=a0-r0
--E 134
--S 135 of 500
--d0:=D(m0,x)
--E 135
)clear all
--S 136 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)
--R
--R
--R              2          +--------+ +------+
--R        (- 10x  - x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------------
--R              3      2            +------+
--R          (27x  + 54x  + 36x + 8)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 136
--S 137 of 500
--r0:=-2/15*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)+_
--     1184/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     4418/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+74/45*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+_
--     988/945*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 137
--S 138 of 500
--a0:=integrate(t0,x)
--E 138
--S 139 of 500
--m0:=a0-r0
--E 139
--S 140 of 500
--d0:=D(m0,x)

--E 140
)clear all
--S 141 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)
--R
--R
--R                 2          +--------+ +------+
--R           (- 10x  - x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------------------
--R            4       3       2             +------+
--R        (81x  + 216x  + 216x  + 96x + 16)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 141
--S 142 of 500
--r0:=-2/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)-_
--     124/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     119732/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+74/105*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-_
--     3632/6615*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     119732/46305*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 142
--S 143 of 500
--a0:=integrate(t0,x)
--E 143
--S 144 of 500
--m0:=a0-r0
--E 144
--S 145 of 500
--d0:=D(m0,x)
--E 145
)clear all
--S 146 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)
--R
--R
--R                       2          +--------+ +------+
--R                 (- 10x  - x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  -----------------------------------------------------
--R             5       4        3       2              +------+
--R        (243x  + 810x  + 1080x  + 720x  + 240x + 32)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 146

--S 147 of 500
--r0:=-2/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)+_
--     561808/250047*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-19885156/250047*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+74/189*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/(2+3*x)^(7/2)-8252/19845*sqrt(1-2*x)*sqrt(3+5*x)/_
--     (2+3*x)^(5/2)+280904/416745*sqrt(1-2*x)*sqrt(3+5*x)/_
--     (2+3*x)^(3/2)+19885156/2917215*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 147
--S 148 of 500
--a0:=integrate(t0,x)
--E 148
--S 149 of 500
--m0:=a0-r0
--E 149
--S 150 of 500
--d0:=D(m0,x)
--E 150
)clear all
--S 151 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2)
--R
--R
--R                            2          +--------+ +------+
--R                      (- 10x  - x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  ----------------------------------------------------------------
--R             6        5        4        3        2              +------+
--R        (729x  + 2916x  + 4860x  + 4320x  + 2160x  + 576x + 64)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 151
--S 152 of 500
--r0:=-2/33*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)+_
--     41599832/6417873*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-1446357824/6417873*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+74/297*(3+5*x)^(3/2)*sqrt(1-2*x)/_
--     (2+3*x)^(9/2)-12872/43659*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
--     442076/1528065*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
--     20799916/10696455*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     1446357824/74875185*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 152
--S 153 of 500
--a0:=integrate(t0,x)

--E 153
--S 154 of 500
--m0:=a0-r0
--E 154
--S 155 of 500
--d0:=D(m0,x)
--E 155
)clear all
--S 156 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)
--R
--R
--R   (1)
--R          5       4       3      2              +--------+ +------+ +------+
--R   (- 450x  - 915x  - 512x  + 85x  + 156x + 36)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 156
--S 157 of 500
--r0:=2/75*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(7/2)+_
--     48128081531/3909262500*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-836091184171/1954631250*_
--     elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
--     2503/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)+_
--     178/14625*(2+3*x)^(5/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_
--     380132617/506756250*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     57509209/506756250*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     199721/12065625*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     50299451003/9121612500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 157
--S 158 of 500
--a0:=integrate(t0,x)
--E 158
--S 159 of 500
--m0:=a0-r0
--E 159
--S 160 of 500
--d0:=D(m0,x)
--E 160
)clear all
--S 161 of 500

t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)
--R
--R
--R               4       3      2             +--------+ +------+ +------+
--R   (1)  (- 150x  - 205x  - 34x  + 51x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 161
--S 162 of 500
--r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_
--     134992031/26061750*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-9380126059/52123500*_
--     elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
--     62/3575*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_
--     2133359/6756750*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     160084/3378375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     67/160875*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     70536439/30405375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 162
--S 163 of 500
--a0:=integrate(t0,x)
--E 163
--S 164 of 500
--m0:=a0-r0
--E 164
--S 165 of 500
--d0:=D(m0,x)
--E 165
)clear all
--S 166 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)
--R
--R
--R              3      2            +--------+ +------+ +------+
--R   (1)  (- 50x  - 35x  + 12x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 166
--S 167 of 500
--r0:=2810993/1202850*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-97540001/1202850*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+2/55*(1-2*x)^(3/2)*(3+5*x)^(7/2)*_
--     sqrt(2+3*x)-22576/155925*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     2377/155925*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
--     194/7425*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_

--S 168 of 500
--a0:=integrate(t0,x)
--E 168
--S 169 of 500
--m0:=a0-r0
--E 169
--S 170 of 500
--d0:=D(m0,x)
--E 170
)clear all
--S 171 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)
--R
--R
--R              3      2            +--------+ +------+
--R        (- 50x  - 35x  + 12x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  ---------------------------------------------
--R                           +------+
--R                          \|3x + 2
--R                                                    Type: Expression(Integer)
--E 171
--S 172 of 500
--r0:=14101/10935*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     886499/21870*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_
--     499/2835*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
--     46/567*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     11908/25515*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 172
--S 173 of 500
--a0:=integrate(t0,x)
--E 173
--S 174 of 500
--m0:=a0-r0
--E 174
--S 175 of 500
--d0:=D(m0,x)
--E 175

--S 176 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)
--R
--R
--R              3      2            +--------+ +------+
--R        (- 50x  - 35x  + 12x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  ---------------------------------------------
--R                               +------+
--R                      (3x + 2)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 176
--S 177 of 500
--r0:=-835/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     2894/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)-2/3*(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)+_
--     202/63*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     32/63*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     1061/567*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 177
--S 178 of 500
--a0:=integrate(t0,x)
--E 178
--S 179 of 500
--m0:=a0-r0
--E 179
--S 180 of 500
--d0:=D(m0,x)
--E 180
)clear all
--S 181 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)
--R
--R
--R              3      2            +--------+ +------+
--R        (- 50x  - 35x  + 12x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  ---------------------------------------------
--R                      2            +------+
--R                   (9x  + 12x + 4)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 181
--S 182 of 500

--r0:=-2/9*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)-_
--     9587/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+21206/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+362/27*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)-_
--     614/27*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+2632/243*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 182
--S 183 of 500
--a0:=integrate(t0,x)
--E 183
--S 184 of 500
--m0:=a0-r0
--E 184
--S 185 of 500
--d0:=D(m0,x)
--E 185
)clear all
--S 186 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)
--R
--R
--R              3      2            +--------+ +------+
--R        (- 50x  - 35x  + 12x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  ---------------------------------------------
--R                   3      2            +------+
--R               (27x  + 54x  + 36x + 8)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 186
--S 187 of 500
--r0:=-2/15*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)-_
--     47422/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+116854/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+362/135*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+_
--     9808/945*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-_
--     43214/1701*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 187
--S 188 of 500
--a0:=integrate(t0,x)
--E 188
--S 189 of 500
--m0:=a0-r0
--E 189

--S 190 of 500
--d0:=D(m0,x)
--E 190
)clear all
--S 191 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)
--R
--R
--R              3      2            +--------+ +------+
--R        (- 50x  - 35x  + 12x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  ---------------------------------------------
--R              4       3       2             +------+
--R          (81x  + 216x  + 216x  + 96x + 16)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 191
--S 192 of 500
--r0:=-2/21*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)+_
--     290204/11907*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-962678/11907*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+2108/6615*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/(2+3*x)^(3/2)+362/315*(3+5*x)^(5/2)*_
--     sqrt(1-2*x)/(2+3*x)^(5/2)+249448/138915*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 192
--S 193 of 500
--a0:=integrate(t0,x)
--E 193
--S 194 of 500
--m0:=a0-r0
--E 194
--S 195 of 500
--d0:=D(m0,x)
--E 195
)clear all
--S 196 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)
--R
--R
--R                  3      2            +--------+ +------+
--R            (- 50x  - 35x  + 12x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  -----------------------------------------------------

--R             5       4        3       2              +------+
--R        (243x  + 810x  + 1080x  + 720x  + 240x + 32)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 196
--S 197 of 500
--r0:=-2/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)-_
--     600868/750141*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-17830424/750141*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)-1864/6615*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/(2+3*x)^(5/2)+362/567*(3+5*x)^(5/2)*_
--     sqrt(1-2*x)/(2+3*x)^(7/2)-558524/1250235*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)+17830424/8751645*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 197
--S 198 of 500
--a0:=integrate(t0,x)
--E 198
--S 199 of 500
--m0:=a0-r0
--E 199
--S 200 of 500
--d0:=D(m0,x)
--E 200
)clear all
--S 201 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)
--R
--R
--R                        3      2            +--------+ +------+
--R                  (- 50x  - 35x  + 12x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  ----------------------------------------------------------------
--R             6        5        4        3        2              +------+
--R        (729x  + 2916x  + 4860x  + 4320x  + 2160x  + 576x + 64)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 201
--S 202 of 500
--r0:=-2/33*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)+_
--     91496584/57760857*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-3316711588/57760857*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)-13292/43659*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/(2+3*x)^(7/2)+362/891*(3+5*x)^(5/2)*sqrt(1-2*x)/_
--     (2+3*x)^(9/2)-1366496/4584195*sqrt(1-2*x)*sqrt(3+5*x)/_
--     (2+3*x)^(5/2)+45748292/96268095*sqrt(1-2*x)*sqrt(3+5*x)/_

--     (2+3*x)^(3/2)+3316711588/673876665*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 202
--S 203 of 500
--a0:=integrate(t0,x)
--E 203
--S 204 of 500
--m0:=a0-r0
--E 204
--S 205 of 500
--d0:=D(m0,x)
--E 205
)clear all
--S 206 of 500
t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2)
--R
--R
--R   (1)
--R           3      2            +--------+ +------+
--R     (- 50x  - 35x  + 12x + 9)\|- 2x + 1 \|5x + 3
--R  /
--R             7         6         5         4         3        2
--R       (2187x  + 10206x  + 20412x  + 22680x  + 15120x  + 6048x  + 1344x + 128)
--R    *
--R        +------+
--R       \|3x + 2
--R                                                    Type: Expression(Integer)
--E 206
--S 207 of 500
--r0:=-2/39*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_
--     7046965448/1752079329*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-245282464136/1752079329*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)-20992/81081*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/(2+3*x)^(9/2)+362/1287*(3+5*x)^(5/2)*_
--     sqrt(1-2*x)/(2+3*x)^(11/2)-2174468/11918907*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(7/2)+73596464/417161745*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(5/2)+3523482724/2920132215*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)+245282464136/20440925505*_
--     sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 207
--S 208 of 500
--a0:=integrate(t0,x)
--E 208

--S 209 of 500
--m0:=a0-r0
--E 209
--S 210 of 500
--d0:=D(m0,x)
--E 210
)clear all
--S 211 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)
--R
--R
--R              3      2           +--------+ +------+
--R        (- 18x  - 15x  + 4x + 4)\|- 2x + 1 \|3x + 2
--R   (1)  --------------------------------------------
--R                           +------+
--R                          \|5x + 3
--R                                                    Type: Expression(Integer)
--E 211
--S 212 of 500
--r0:=87476/253125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-6515539/506250*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+2/45*(1-2*x)^(3/2)*(2+3*x)^(5/2)*_
--     sqrt(3+5*x)+403/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     178/4725*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-87476/590625*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 212
--S 213 of 500
--a0:=integrate(t0,x)
--E 213
--S 214 of 500
--m0:=a0-r0
--E 214
--S 215 of 500
--d0:=D(m0,x)
--E 215
)clear all
--S 216 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/sqrt(3+5*x)
--R
--R
--R             2          +--------+ +------+

--R        (- 6x  - x + 2)\|- 2x + 1 \|3x + 2
--R   (1)  -----------------------------------
--R                      +------+
--R                     \|5x + 3
--R                                                    Type: Expression(Integer)
--E 216
--S 217 of 500
--r0:=487/5625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     46159/5625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/35*(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)+_
--     62/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-487/13125*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 217
--S 218 of 500
--a0:=integrate(t0,x)
--E 218
--S 219 of 500
--m0:=a0-r0
--E 219
--S 220 of 500
--d0:=D(m0,x)
--E 220
)clear all
--S 221 of 500
t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)
--R
--R
--R                   +--------+ +------+
--R        (- 2x + 1)\|- 2x + 1 \|3x + 2
--R   (1)  ------------------------------
--R                    +------+
--R                   \|5x + 3
--R                                                    Type: Expression(Integer)
--E 221
--S 222 of 500
--r0:=-2797/3375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-2828/3375*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+2/25*(1-2*x)^(3/2)*sqrt(2+3*x)*_
--     sqrt(3+5*x)+194/1125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 222
--S 223 of 500
--a0:=integrate(t0,x)

--E 223
--S 224 of 500
--m0:=a0-r0
--E 224
--S 225 of 500
--d0:=D(m0,x)
--E 225
)clear all
--S 226 of 500
t0:=(1-2*x)^(3/2)/(sqrt(2+3*x)*sqrt(3+5*x))
--R
--R
--R                   +--------+
--R        (- 2x + 1)\|- 2x + 1
--R   (1)  ---------------------
--R           +------+ +------+
--R          \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 226
--S 227 of 500
--r0:=272/135*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     1442/135*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-4/45*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 227
--S 228 of 500
--a0:=integrate(t0,x)
--E 228
--S 229 of 500
--m0:=a0-r0
--E 229
--S 230 of 500
--d0:=D(m0,x)
--E 230
)clear all
--S 231 of 500
t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*sqrt(3+5*x))
--R
--R
--R                      +--------+
--R           (- 2x + 1)\|- 2x + 1

--R   (1)  --------------------------
--R                 +------+ +------+
--R        (3x + 2)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 231
--S 232 of 500
--r0:=-74/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
--     56/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)+4/3*sqrt(1-2*x)*_
--     sqrt(2+3*x)*sqrt(3+5*x)
--E 232
--S 233 of 500
--a0:=integrate(t0,x)
--E 233
--S 234 of 500
--m0:=a0-r0
--E 234
--S 235 of 500
--d0:=D(m0,x)
--E 235
)clear all
--S 236 of 500
t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*sqrt(3+5*x))
--R
--R
--R                         +--------+
--R              (- 2x + 1)\|- 2x + 1
--R   (1)  ---------------------------------
--R           2            +------+ +------+
--R        (9x  + 12x + 4)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 236
--S 237 of 500
--r0:=116/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     124/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(35)+2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     128/9*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 237
--S 238 of 500
--a0:=integrate(t0,x)
--E 238

--S 240 of 500
--d0:=D(m0,x)
--E 240
)clear all
--S 241 of 500
t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x))
--R
--R
--R                             +--------+
--R                  (- 2x + 1)\|- 2x + 1
--R   (1)  -----------------------------------------
--R            3      2            +------+ +------+
--R        (27x  + 54x  + 36x + 8)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 241
--S 242 of 500
--r0:=512/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     17804/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/5*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
--     268/45*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+17804/315*_
--     sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 242
--S 243 of 500
--a0:=integrate(t0,x)
--E 243
--S 244 of 500
--m0:=a0-r0
--E 244
--S 245 of 500
--d0:=D(m0,x)
--E 245
)clear all
--S 246 of 500
t0:=(1-2*x)^(3/2)/((2+3*x)^(9/2)*sqrt(3+5*x))
--R
--R
--R                                  +--------+
--R                       (- 2x + 1)\|- 2x + 1

--R   (1)  ---------------------------------------------------
--R            4       3       2             +------+ +------+
--R        (81x  + 216x  + 216x  + 96x + 16)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 246
--S 247 of 500
--r0:=36136/441*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     1255552/441*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/7*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
--     136/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+18068/735*_
--     sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+1255552/5145*_
--     sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 247
--S 248 of 500
--a0:=integrate(t0,x)
--E 248
--S 249 of 500
--m0:=a0-r0
--E 249
--S 250 of 500
--d0:=D(m0,x)
--E 250
)clear all
--S 251 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)
--R
--R
--R              4      3      2            +--------+ +------+
--R        (- 54x  - 81x  - 18x  + 20x + 8)\|- 2x + 1 \|3x + 2
--R   (1)  ----------------------------------------------------
--R                                   +------+
--R                          (5x + 3)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 251
--S 252 of 500
--r0:=12601/84375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-1473539/168750*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(3/2)*(2+3*x)^(7/2)/_
--     sqrt(3+5*x)+5153/39375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     958/1575*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-8/45*(2+3*x)^(7/2)*_
--     sqrt(1-2*x)*sqrt(3+5*x)-12601/196875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 252

--S 254 of 500
--m0:=a0-r0
--E 254
--S 255 of 500
--d0:=D(m0,x)
--E 255
)clear all
--S 256 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)
--R
--R
--R              3      2           +--------+ +------+
--R        (- 18x  - 15x  + 4x + 4)\|- 2x + 1 \|3x + 2
--R   (1)  --------------------------------------------
--R                               +------+
--R                      (5x + 3)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 256
--S 257 of 500
--r0:=-2719/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     47342/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)-2/5*(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)+_
--     2818/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
--     32/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     2719/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 257
--S 258 of 500
--a0:=integrate(t0,x)
--E 258
--S 259 of 500
--m0:=a0-r0
--E 259
--S 260 of 500
--d0:=D(m0,x)
--E 260
)clear all
--S 261 of 500

t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)
--R
--R
--R             2          +--------+ +------+
--R        (- 6x  - x + 2)\|- 2x + 1 \|3x + 2
--R   (1)  -----------------------------------
--R                          +------+
--R                 (5x + 3)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 261
--S 262 of 500
--r0:=-169/1875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-3206/1875*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-2/5*(1-2*x)^(3/2)*(2+3*x)^(3/2)/_
--     sqrt(3+5*x)-24/125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     458/625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 262
--S 263 of 500
--a0:=integrate(t0,x)
--E 263
--S 264 of 500
--m0:=a0-r0
--E 264
--S 265 of 500
--d0:=D(m0,x)
--E 265
)clear all
--S 266 of 500
t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)
--R
--R
--R                   +--------+ +------+
--R        (- 2x + 1)\|- 2x + 1 \|3x + 2
--R   (1)  ------------------------------
--R                        +------+
--R               (5x + 3)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 266
--S 267 of 500
--r0:=458/225*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     1358/225*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-2/5*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-_
--     16/75*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)

--E 267
--S 268 of 500
--a0:=integrate(t0,x)
--E 268
--S 269 of 500
--m0:=a0-r0
--E 269
--S 270 of 500
--d0:=D(m0,x)
--E 270
)clear all
--S 271 of 500
t0:=(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x))
--R
--R
--R                      +--------+
--R           (- 2x + 1)\|- 2x + 1
--R   (1)  --------------------------
--R                 +------+ +------+
--R        (5x + 3)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 271
--S 272 of 500
--r0:=62/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
--     28/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     2*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-4/5*sqrt(1-2*x)*_
--     sqrt(2+3*x)*sqrt(3+5*x)
--E 272
--S 273 of 500
--a0:=integrate(t0,x)
--E 273
--S 274 of 500
--m0:=a0-r0
--E 274
--S 275 of 500
--d0:=D(m0,x)
--E 275
)clear all
--S 276 of 500

t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))
--R
--R
--R                          +--------+
--R               (- 2x + 1)\|- 2x + 1
--R   (1)  ----------------------------------
--R            2            +------+ +------+
--R        (15x  + 19x + 6)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 276
--S 277 of 500
--r0:=136/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     28/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2*(1-2*x)^(3/2)/(sqrt(2+3*x)*sqrt(3+5*x))-44*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 277
--S 278 of 500
--a0:=integrate(t0,x)
--E 278
--S 279 of 500
--m0:=a0-r0
--E 279
--S 280 of 500
--d0:=D(m0,x)
--E 280
)clear all
--S 281 of 500
t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))
--R
--R
--R                              +--------+
--R                   (- 2x + 1)\|- 2x + 1
--R   (1)  ------------------------------------------
--R            3      2             +------+ +------+
--R        (45x  + 87x  + 56x + 12)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 281
--S 282 of 500
--r0:=-536/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     532/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(35)+2/3*(1-2*x)^(3/2)/((2+3*x)^(3/2)*sqrt(3+5*x))+_
--     268/9*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2660/9*_
--     sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)

--E 282
--S 283 of 500
--a0:=integrate(t0,x)
--E 283
--S 284 of 500
--m0:=a0-r0
--E 284
--S 285 of 500
--d0:=D(m0,x)
--E 285
)clear all
--S 286 of 500
t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2))
--R
--R
--R                                   +--------+
--R                        (- 2x + 1)\|- 2x + 1
--R   (1)  -----------------------------------------------------
--R             4       3       2              +------+ +------+
--R        (135x  + 351x  + 342x  + 148x + 24)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 286
--S 287 of 500
--r0:=-1064/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     36968/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/5*(1-2*x)^(3/2)/((2+3*x)^(5/2)*sqrt(3+5*x))+_
--     136/15*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+6116/35*_
--     sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-36968/21*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 287
--S 288 of 500
--a0:=integrate(t0,x)
--E 288
--S 289 of 500
--m0:=a0-r0
--E 289
--S 290 of 500
--d0:=D(m0,x)
--E 290
)clear all

--S 291 of 500
t0:=(1-2*x)^(3/2)/((2+3*x)^(9/2)*(3+5*x)^(3/2))
--R
--R
--R                                         +--------+
--R                              (- 2x + 1)\|- 2x + 1
--R   (1)  ----------------------------------------------------------------
--R             5        4        3        2              +------+ +------+
--R        (405x  + 1323x  + 1728x  + 1128x  + 368x + 48)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 291
--S 292 of 500
--r0:=-296816/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     10312712/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2/7*(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+_
--     548/105*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+12276/245*_
--     sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+1706144/1715*_
--     sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-10312712/1029*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 292
--S 293 of 500
--a0:=integrate(t0,x)
--E 293
--S 294 of 500
--m0:=a0-r0
--E 294
--S 295 of 500
--d0:=D(m0,x)
--E 295
)clear all
--S 296 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2)
--R
--R
--R              4      3      2            +--------+ +------+
--R        (- 54x  - 81x  - 18x  + 20x + 8)\|- 2x + 1 \|3x + 2
--R   (1)  ----------------------------------------------------
--R                          2            +------+
--R                      (25x  + 30x + 9)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 296
--S 297 of 500

--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)-_
--     4801/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     25643/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)-6*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
--     3872/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     622/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     4801/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 297
--S 298 of 500
--a0:=integrate(t0,x)
--E 298
--S 299 of 500
--m0:=a0-r0
--E 299
--S 300 of 500
--d0:=D(m0,x)
--E 300
)clear all
--S 301 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2)
--R
--R
--R              3      2           +--------+ +------+
--R        (- 18x  - 15x  + 4x + 4)\|- 2x + 1 \|3x + 2
--R   (1)  --------------------------------------------
--R                      2            +------+
--R                  (25x  + 30x + 9)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 301
--S 302 of 500
--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)+_
--     1973/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-15848/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-106/25*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
--     1558/625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+2264/3125*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 302
--S 303 of 500
--a0:=integrate(t0,x)
--E 303
--S 304 of 500
--m0:=a0-r0

--E 304
--S 305 of 500
--d0:=D(m0,x)
--E 305
)clear all
--S 306 of 500
t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2)
--R
--R
--R             2          +--------+ +------+
--R        (- 6x  - x + 2)\|- 2x + 1 \|3x + 2
--R   (1)  -----------------------------------
--R                 2            +------+
--R             (25x  + 30x + 9)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 306
--S 307 of 500
--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)+_
--     496/375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-1246/375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-62/25*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_
--     178/125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 307
--S 308 of 500
--a0:=integrate(t0,x)
--E 308
--S 309 of 500
--m0:=a0-r0
--E 309
--S 310 of 500
--d0:=D(m0,x)
--E 310
)clear all
--S 311 of 500
t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(5/2)
--R
--R
--R                   +--------+ +------+
--R        (- 2x + 1)\|- 2x + 1 \|3x + 2
--R   (1)  ------------------------------
--R               2            +------+

--R           (25x  + 30x + 9)\|5x + 3
--R                                                    Type: Expression(Integer)
--E 311
--S 312 of 500
--r0:=38/75*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
--     112/75*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     2/15*(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)-_
--     18/25*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 312
--S 313 of 500
--a0:=integrate(t0,x)
--E 313
--S 314 of 500
--m0:=a0-r0
--E 314
--S 315 of 500
--d0:=D(m0,x)
--E 315
)clear all
--S 316 of 500
t0:=(1-2*x)^(3/2)/((3+5*x)^(5/2)*sqrt(2+3*x))
--R
--R
--R                          +--------+
--R               (- 2x + 1)\|- 2x + 1
--R   (1)  ----------------------------------
--R            2            +------+ +------+
--R        (25x  + 30x + 9)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 316
--S 317 of 500
--r0:=-148/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
--     28/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     2/3*(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)+48/5*sqrt(1-2*x)*_
--     sqrt(2+3*x)/sqrt(3+5*x)
--E 317
--S 318 of 500
--a0:=integrate(t0,x)
--E 318
--S 319 of 500
--m0:=a0-r0

--E 319
--S 320 of 500
--d0:=D(m0,x)
--E 320
)clear all
--S 321 of 500
t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(5/2))
--R
--R
--R                              +--------+
--R                   (- 2x + 1)\|- 2x + 1
--R   (1)  -------------------------------------------
--R            3       2             +------+ +------+
--R        (75x  + 140x  + 87x + 18)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 321
--S 322 of 500
--r0:=-556/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_
--     112/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     2*(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-88/3*sqrt(1-2*x)*_
--     sqrt(2+3*x)/(3+5*x)^(3/2)+556/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 322
--S 323 of 500
--a0:=integrate(t0,x)
--E 323
--S 324 of 500
--m0:=a0-r0
--E 324
--S 325 of 500
--d0:=D(m0,x)
--E 325
)clear all
--S 326 of 500
t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(5/2))
--R
--R
--R                                   +--------+
--R                        (- 2x + 1)\|- 2x + 1
--R   (1)  -----------------------------------------------------
--R             4       3       2              +------+ +------+
--R        (225x  + 570x  + 541x  + 228x + 36)\|3x + 2 \|5x + 3

--R                                                    Type: Expression(Integer)
--E 326
--S 327 of 500
--r0:=2/3*(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
--     1096/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     1088/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_
--     136/3*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-300*sqrt(1-2*x)*_
--     sqrt(2+3*x)/(3+5*x)^(3/2)+5440/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 327
--S 328 of 500
--a0:=integrate(t0,x)
--E 328
--S 329 of 500
--m0:=a0-r0
--E 329
--S 330 of 500
--d0:=D(m0,x)
--E 330
)clear all
--S 331 of 500
t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(5/2))
--R
--R
--R                                         +--------+
--R                              (- 2x + 1)\|- 2x + 1
--R   (1)  ----------------------------------------------------------------
--R             5        4        3        2              +------+ +------+
--R        (675x  + 2160x  + 2763x  + 1766x  + 564x + 72)\|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 331
--S 332 of 500
--r0:=2/5*(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_
--     8672/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     301304/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+548/45*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_
--     111884/315*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_
--     16616/7*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_
--     301304/21*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x)
--E 332
--S 333 of 500
--a0:=integrate(t0,x)
--E 333

--S 335 of 500
--d0:=D(m0,x)
--E 335
)clear all
--S 336 of 500
t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x)
--R
--R
--R            4      3      2           +--------+ +------+ +------+
--R   (1)  (36x  + 12x  - 23x  - 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 336
--S 337 of 500
--r0:=62/2145*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+_
--     2/65*(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+_
--     67138787/72393750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-1163388067/36196875*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+32717/1126125*(2+3*x)^(3/2)*_
--     (3+5*x)^(3/2)*sqrt(1-2*x)+34/2475*(2+3*x)^(5/2)*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)-445024/9384375*(3+5*x)^(3/2)*sqrt(1-2*x)*_
--     sqrt(2+3*x)-69808931/168918750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 337
--S 338 of 500
--a0:=integrate(t0,x)
--E 338
--S 339 of 500
--m0:=a0-r0
--E 339
--S 340 of 500
--d0:=D(m0,x)
--E 340
)clear all
--S 341 of 500
t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x)
--R
--R
--R            3     2           +--------+ +------+ +------+

--R   (1)  (12x  - 4x  - 5x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 341
--S 342 of 500
--r0:=106/2475*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)+2/55*(1-2*x)^(5/2)*_
--     (2+3*x)^(3/2)*(3+5*x)^(3/2)+4854274/8353125*_
--     elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     326256461/16706250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+2866/86625*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+_
--     38729/2165625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     4738087/19490625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 342
--S 343 of 500
--a0:=integrate(t0,x)
--E 343
--S 344 of 500
--m0:=a0-r0
--E 344
--S 345 of 500
--d0:=D(m0,x)
--E 345
)clear all
--S 346 of 500
t0:=(1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x)
--R
--R
--R           2           +--------+ +------+ +------+
--R   (1)  (4x  - 4x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 346
--S 347 of 500
--r0:=284159/455625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-6799613/455625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+326/4725*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_
--     2/45*(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_
--     10214/118125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     110717/1063125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 347
--S 348 of 500
--a0:=integrate(t0,x)
--E 348

--S 350 of 500
--d0:=D(m0,x)
--E 350
)clear all
--S 351 of 500
t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x)
--R
--R
--R           2           +--------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  ----------------------------------
--R                      +------+
--R                     \|3x + 2
--R                                                    Type: Expression(Integer)
--E 351
--S 352 of 500
--r0:=16088/3375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     86741/3375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_
--     118/525*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+2/21*(1-2*x)^(5/2)*_
--     sqrt(2+3*x)*sqrt(3+5*x)+4282/7875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 352
--S 353 of 500
--a0:=integrate(t0,x)
--E 353
--S 354 of 500
--m0:=a0-r0
--E 354
--S 355 of 500
--d0:=D(m0,x)
--E 355
)clear all
--S 356 of 500
t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2)
--R
--R
--R           2           +--------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  ----------------------------------

--R                          +------+
--R                 (3x + 2)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 356
--S 357 of 500
--r0:=31588/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-96838/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-2/3*(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x)-_
--     8/15*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)-1076/675*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 357
--S 358 of 500
--a0:=integrate(t0,x)
--E 358
--S 359 of 500
--m0:=a0-r0
--E 359
--S 360 of 500
--d0:=D(m0,x)
--E 360
)clear all
--S 361 of 500
t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2)
--E 361
--S 362 of 500
--r0:=-4418/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+8288/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-2/9*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     10/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)+196/81*sqrt(1-2*x)*_
--     sqrt(2+3*x)*sqrt(3+5*x)
--E 362
--S 363 of 500
--Ra0:=integrate(t0,x)
--R
--R
--R   (1)  t0 x
--R                                          Type: Polynomial(Fraction(Integer))
--E 363
--S 364 of 500
--Rm0:=a0-r0
--R

--R
--R   (2)  t0 x - r0
--R                                          Type: Polynomial(Fraction(Integer))
--E 364
--S 365 of 500
--Rd0:=D(m0,x)
--R
--R
--R   (3)  t0
--R                                          Type: Polynomial(Fraction(Integer))
--E 365
)clear all
--S 366 of 500
t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2)
--R
--R
--R           2           +--------+ +------+
--R        (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  ----------------------------------
--R             3      2            +------+
--R         (27x  + 54x  + 36x + 8)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 366
--S 367 of 500
--r0:=-12*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     2/15*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+2/3*(1-2*x)^(3/2)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)+8*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 367
--S 368 of 500
--a0:=integrate(t0,x)
--E 368
--S 369 of 500
--m0:=a0-r0
--E 369
--S 370 of 500
--d0:=D(m0,x)
--E 370
)clear all
--S 371 of 500
t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(9/2)

--R
--R
--R               2           +--------+ +------+
--R            (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------------------
--R            4       3       2             +------+
--R        (81x  + 216x  + 216x  + 96x + 16)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 371
--S 372 of 500
--r0:=-36052/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     5360/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-2/21*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+2/7*_
--     (1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+524/189*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)+36052/1323*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 372
--S 373 of 500
--a0:=integrate(t0,x)
--E 373
--S 374 of 500
--m0:=a0-r0
--E 374
--S 375 of 500
--d0:=D(m0,x)
--E 375
)clear all
--S 376 of 500
t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(11/2)
--R
--R
--R                     2           +--------+ +------+
--R                  (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  -----------------------------------------------------
--R             5       4        3       2              +------+
--R        (243x  + 810x  + 1080x  + 720x  + 240x + 32)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 376
--S 377 of 500
--r0:=-7810384/35721*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)+1124360/35721*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-2/27*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_
--     10/63*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+832/567*_
--     sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+112436/11907*sqrt(1-2*x)*_

--     sqrt(3+5*x)/(2+3*x)^(3/2)+7810384/83349*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 377
--S 378 of 500
--a0:=integrate(t0,x)
--E 378
--S 379 of 500
--m0:=a0-r0
--E 379
--S 380 of 500
--d0:=D(m0,x)
--E 380
)clear all
--S 381 of 500
t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(13/2)
--R
--R
--R                          2           +--------+ +------+
--R                       (4x  - 4x + 1)\|- 2x + 1 \|5x + 3
--R   (1)  ----------------------------------------------------------------
--R             6        5        4        3        2              +------+
--R        (729x  + 2916x  + 4860x  + 4320x  + 2160x  + 576x + 64)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 381
--S 382 of 500
--r0:=-247408648/305613*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)+35604320/305613*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-2/33*(1-2*x)^(5/2)*sqrt(3+5*x)/_
--     (2+3*x)^(11/2)+10/99*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_
--     1900/2079*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
--     76492/14553*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
--     3560432/101871*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     247408648/713097*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 382
--S 383 of 500
--a0:=integrate(t0,x)
--E 383
--S 384 of 500
--m0:=a0-r0
--E 384
--S 385 of 500

--d0:=D(m0,x)
--E 385
)clear all
--S 386 of 500
t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)
--R
--R
--R             5       4      3      2            +--------+ +------+ +------+
--R   (1)  (180x  + 168x  - 79x  - 89x  + 8x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 386
--S 387 of 500
--r0:=62/2925*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)+2/75*(1-2*x)^(5/2)*_
--     (2+3*x)^(5/2)*(3+5*x)^(5/2)+25385346787/9773156250*_
--     elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     1764163292393/19546312500*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+142391/7239375*(2+3*x)^(3/2)*_
--     (3+5*x)^(5/2)*sqrt(1-2*x)+3698/482625*(2+3*x)^(5/2)*(3+5*x)^(5/2)*_
--     sqrt(1-2*x)-400516993/2533781250*(3+5*x)^(3/2)*sqrt(1-2*x)*_
--     sqrt(2+3*x)-569519/28153125*(3+5*x)^(5/2)*sqrt(1-2*x)*_
--     sqrt(2+3*x)-13267820528/11402015625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 387
--S 388 of 500
--a0:=integrate(t0,x)
--E 388
--S 389 of 500
--m0:=a0-r0
--E 389
--S 390 of 500
--d0:=D(m0,x)
--E 390
)clear all
--S 391 of 500
t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)
--R
--R
--R            4      3      2           +--------+ +------+ +------+
--R   (1)  (60x  + 16x  - 37x  - 5x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 391
--S 392 of 500

--r0:=106/3575*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+_
--     2/65*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+_
--     880870681/651543750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-30660308017/651543750*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+8318/482625*(2+3*x)^(3/2)*(3+5*x)^(5/2)*_
--     sqrt(1-2*x)-6794792/84459375*(3+5*x)^(3/2)*sqrt(1-2*x)*_
--     sqrt(2+3*x)+25603/1876875*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     923943703/1520268750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 392
--S 393 of 500
--a0:=integrate(t0,x)
--E 393
--S 394 of 500
--m0:=a0-r0
--E 394
--S 395 of 500
--d0:=D(m0,x)
--E 395
)clear all
--S 396 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)
--R
--R
--R            3     2           +--------+ +------+ +------+
--R   (1)  (20x  - 8x  - 7x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 396
--S 397 of 500
--r0:=11437073/15035625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-829177897/30071250*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+326/7425*(1-2*x)^(3/2)*_
--     (3+5*x)^(5/2)*sqrt(2+3*x)+2/55*(1-2*x)^(5/2)*(3+5*x)^(5/2)*_
--     sqrt(2+3*x)-78797/3898125*(3+5*x)^(3/2)*sqrt(1-2*x)*_
--     sqrt(2+3*x)+30362/779625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     12996374/35083125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 397
--S 398 of 500
--a0:=integrate(t0,x)
--E 398
--S 399 of 500
--m0:=a0-r0
--E 399

)clear all
--S 401 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/sqrt(2+3*x)
--R
--R
--R            3     2           +--------+ +------+
--R        (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  -----------------------------------------
--R                         +------+
--R                        \|3x + 2
--R                                                    Type: Expression(Integer)
--E 401
--S 402 of 500
--r0:=-150217/273375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-4457606/273375*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+362/2835*(1-2*x)^(3/2)*(3+5*x)^(3/2)*_
--     sqrt(2+3*x)+2/27*(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_
--     14318/70875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     429479/637875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 402
--S 403 of 500
--a0:=integrate(t0,x)
--E 403
--S 404 of 500
--m0:=a0-r0
--E 404
--S 405 of 500
--d0:=D(m0,x)
--E 405
)clear all
--S 406 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)
--R
--R
--R            3     2           +--------+ +------+
--R        (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  -----------------------------------------
--R                             +------+

--R                    (3x + 2)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 406
--S 407 of 500
--r0:=145102/6075*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     481339/6075*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)-2/3*(1-2*x)^(5/2)*(3+5*x)^(3/2)/sqrt(2+3*x)-_
--     32/63*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)-_
--     2108/1575*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
--     124724/14175*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 407
--S 408 of 500
--a0:=integrate(t0,x)
--E 408
--S 409 of 500
--m0:=a0-r0
--E 409
--S 410 of 500
--d0:=D(m0,x)
--E 410
)clear all
--S 411 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)
--R
--R
--R            3     2           +--------+ +------+
--R        (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  -----------------------------------------
--R                    2            +------+
--R                 (9x  + 12x + 4)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 411
--S 412 of 500
--r0:=-2/9*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)+116854/3645*_
--     elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_
--     331954/3645*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+230/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)+_
--     788/135*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-43214/1215*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 412
--S 413 of 500
--a0:=integrate(t0,x)

--E 413
--S 414 of 500
--m0:=a0-r0
--E 414
--S 415 of 500
--d0:=D(m0,x)
--E 415
)clear all
--S 416 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)
--R
--R
--R            3     2           +--------+ +------+
--R        (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  -----------------------------------------
--R                 3      2            +------+
--R             (27x  + 54x  + 36x + 8)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 416
--S 417 of 500
--r0:=-2/15*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)+_
--     46/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)-_
--     19174/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)+42412/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-316/27*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+5264/243*_
--     sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 417
--S 418 of 500
--a0:=integrate(t0,x)
--E 418
--S 419 of 500
--m0:=a0-r0
--E 419
--S 420 of 500
--d0:=D(m0,x)
--E 420
)clear all
--S 421 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)
--R

--R
--R             3     2           +--------+ +------+
--R         (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  ------------------------------------------
--R            4       3       2             +------+
--R        (81x  + 216x  + 216x  + 96x + 16)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 421
--S 422 of 500
--r0:=-2/21*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)+_
--     46/63*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)-_
--     11576/1701*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)-16700/1701*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)+608/189*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_
--     4244/3969*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 422
--S 423 of 500
--a0:=integrate(t0,x)
--E 423
--S 424 of 500
--m0:=a0-r0
--E 424
--S 425 of 500
--d0:=D(m0,x)
--E 425
)clear all
--S 426 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)
--R
--R
--R                  3     2           +--------+ +------+
--R              (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  -----------------------------------------------------
--R             5       4        3       2              +------+
--R        (243x  + 810x  + 1080x  + 720x  + 240x + 32)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 426
--S 427 of 500
--r0:=-2/27*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)+_
--     230/567*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)-_
--     3545996/107163*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)+564040/107163*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+1532/567*(3+5*x)^(3/2)*_

--     sqrt(1-2*x)/(2+3*x)^(5/2)-104036/35721*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)+3545996/250047*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 427
--S 428 of 500
--a0:=integrate(t0,x)
--E 428
--S 429 of 500
--m0:=a0-r0
--E 429
--S 430 of 500
--d0:=D(m0,x)
--E 430
)clear all
--S 431 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2)
--R
--R
--R                        3     2           +--------+ +------+
--R                    (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R   (1)  ----------------------------------------------------------------
--R             6        5        4        3        2              +------+
--R        (729x  + 2916x  + 4860x  + 4320x  + 2160x  + 576x + 64)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 431
--S 432 of 500
--r0:=-2/33*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)+_
--     230/891*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)-_
--     780320008/8251551*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)+112439720/8251551*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)+12280/6237*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/(2+3*x)^(7/2)-325796/130977*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(5/2)+11243972/2750517*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)+780320008/19253619*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 432
--S 433 of 500
--a0:=integrate(t0,x)
--E 433
--S 434 of 500
--m0:=a0-r0
--E 434

)clear all
--S 436 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(15/2)
--R
--R
--R   (1)
--R         3     2           +--------+ +------+
--R     (20x  - 8x  - 7x + 3)\|- 2x + 1 \|5x + 3
--R  /
--R             7         6         5         4         3        2
--R       (2187x  + 10206x  + 20412x  + 22680x  + 15120x  + 6048x  + 1344x + 128)
--R    *
--R        +------+
--R       \|3x + 2
--R                                                    Type: Expression(Integer)
--E 436
--S 437 of 500
--r0:=-2/39*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2)+_
--     230/1287*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)-_
--     75041008472/250297047*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)*sqrt(5/7)+10799362480/250297047*_
--     elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_
--     1300/891*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_
--     3347620/1702701*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
--     23210828/11918907*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
--     1079936248/83432349*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     75041008472/584026443*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 437
--S 438 of 500
--a0:=integrate(t0,x)
--E 438
--S 439 of 500
--m0:=a0-r0
--E 439
--S 440 of 500
--d0:=D(m0,x)
--E 440
)clear all

--S 441 of 500
t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)
--R
--R
--R   (1)
--R        5       4       3       2             +--------+ +------+ +------+
--R   (300x  + 260x  - 137x  - 136x  + 15x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 441
--S 442 of 500
--r0:=106/4875*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_
--     2/75*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_
--     11371367372/2931946875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-1580201444291/11727787500*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+8038/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*_
--     sqrt(1-2*x)-359748241/1520268750*(3+5*x)^(3/2)*sqrt(1-2*x)*_
--     sqrt(2+3*x)-26534891/760134375*(3+5*x)^(5/2)*sqrt(1-2*x)*_
--     sqrt(2+3*x)+364267/36196875*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     23763809947/13682418750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 442
--S 443 of 500
--a0:=integrate(t0,x)
--E 443
--S 444 of 500
--m0:=a0-r0
--E 444
--S 445 of 500
--d0:=D(m0,x)
--E 445
)clear all
--S 446 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)
--R
--R
--R             4      3      2           +--------+ +------+ +------+
--R   (1)  (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3
--R                                                    Type: Expression(Integer)
--E 446
--S 447 of 500
--r0:=469049629/234555750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-8120161139/117277875*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+326/10725*(1-2*x)^(3/2)*(3+5*x)^(7/2)*_
--     sqrt(2+3*x)+2/65*(1-2*x)^(5/2)*(3+5*x)^(7/2)*sqrt(2+3*x)-_

--     3872003/30405375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     121031/30405375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
--     2314/111375*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     486785077/547296750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 447
--S 448 of 500
--a0:=integrate(t0,x)
--E 448
--S 449 of 500
--m0:=a0-r0
--E 449
--S 450 of 500
--d0:=D(m0,x)
--E 450
)clear all
--S 451 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/sqrt(2+3*x)
--R
--R
--R             4      3      2           +--------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  --------------------------------------------------
--R                              +------+
--R                             \|3x + 2
--R                                                    Type: Expression(Integer)
--E 451
--S 452 of 500
--r0:=2617892/1804275*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-146222113/3608550*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+74/891*(1-2*x)^(3/2)*(3+5*x)^(5/2)*_
--     sqrt(2+3*x)+2/33*(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_
--     146963/467775*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
--     9698/93555*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     1654421/4209975*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 452
--S 453 of 500
--a0:=integrate(t0,x)
--E 453
--S 454 of 500
--m0:=a0-r0
--E 454

)clear all
--S 456 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)
--R
--R
--R             4      3      2           +--------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  --------------------------------------------------
--R                                  +------+
--R                         (3x + 2)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 456
--S 457 of 500
--r0:=-291227/32805*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-25111/32805*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)-2/3*(1-2*x)^(5/2)*(3+5*x)^(5/2)/sqrt(2+3*x)-_
--     40/81*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)+_
--     64628/8505*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     2108/1701*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     310399/76545*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 457
--S 458 of 500
--a0:=integrate(t0,x)
--E 458
--S 459 of 500
--m0:=a0-r0
--E 459
--S 460 of 500
--d0:=D(m0,x)
--E 460
)clear all
--S 461 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)
--R
--R
--R             4      3      2           +--------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  --------------------------------------------------
--R                        2            +------+

--S 462 of 500
--r0:=-2/9*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)+_
--     153452/2187*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-452399/2187*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_
--     sqrt(35)+370/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)-_
--     31298/567*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
--     5260/567*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_
--     135334/5103*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 462
--S 463 of 500
--a0:=integrate(t0,x)
--E 463
--S 464 of 500
--m0:=a0-r0
--E 464
--S 465 of 500
--d0:=D(m0,x)
--E 465
)clear all
--S 466 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)
--R
--R
--R             4      3      2           +--------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  --------------------------------------------------
--R                     3      2            +------+
--R                 (27x  + 54x  + 36x + 8)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 466
--S 467 of 500
--r0:=-2/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)+_
--     74/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)+_
--     136028/2187*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(7/5)-374366/2187*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-6464/81*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+_
--     11036/81*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_
--     48478/729*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 467

--S 469 of 500
--m0:=a0-r0
--E 469
--S 470 of 500
--d0:=D(m0,x)
--E 470
)clear all
--S 471 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)
--R
--R
--R             4      3      2           +--------+ +------+
--R        (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  --------------------------------------------------
--R                4       3       2             +------+
--R            (81x  + 216x  + 216x  + 96x + 16)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 471
--S 472 of 500
--r0:=-2/21*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)+_
--     74/63*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)-904798/15309*_
--     elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_
--     1534520/15309*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-1844/567*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_
--     62596/3969*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+_
--     1353340/35721*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 472
--S 473 of 500
--a0:=integrate(t0,x)
--E 473
--S 474 of 500
--m0:=a0-r0
--E 474
--S 475 of 500
--d0:=D(m0,x)
--E 475
)clear all

--S 476 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)
--R
--R
--R               4      3      2           +--------+ +------+
--R          (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  -----------------------------------------------------
--R             5       4        3       2              +------+
--R        (243x  + 810x  + 1080x  + 720x  + 240x + 32)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 476
--S 477 of 500
--r0:=-2/27*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)+_
--     370/567*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)-_
--     100444/321489*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)-5824540/321489*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-13316/35721*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/(2+3*x)^(3/2)+2776/1701*(3+5*x)^(5/2)*_
--     sqrt(1-2*x)/(2+3*x)^(5/2)-1241596/750141*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 477
--S 478 of 500
--a0:=integrate(t0,x)
--E 478
--S 479 of 500
--m0:=a0-r0
--E 479
--S 480 of 500
--d0:=D(m0,x)
--E 480
)clear all
--S 481 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)
--R
--R
--R                    4      3      2           +--------+ +------+
--R               (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R   (1)  ----------------------------------------------------------------
--R             6        5        4        3        2              +------+
--R        (729x  + 2916x  + 4860x  + 4320x  + 2160x  + 576x + 64)\|3x + 2
--R                                                    Type: Expression(Integer)
--E 481
--S 482 of 500

--r0:=-2/33*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)+_
--     370/891*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)-_
--     584888452/24754653*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_
--     sqrt(5/7)+104715680/24754653*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-55772/43659*(3+5*x)^(3/2)*_
--     sqrt(1-2*x)/(2+3*x)^(5/2)+36980/18711*(3+5*x)^(5/2)*_
--     sqrt(1-2*x)/(2+3*x)^(7/2)-17089252/8251551*sqrt(1-2*x)*_
--     sqrt(3+5*x)/(2+3*x)^(3/2)+584888452/57760857*sqrt(1-2*x)*_
--     sqrt(3+5*x)/sqrt(2+3*x)
--E 482
--S 483 of 500
--a0:=integrate(t0,x)
--E 483
--S 484 of 500
--m0:=a0-r0
--E 484
--S 485 of 500
--d0:=D(m0,x)
--E 485
)clear all
--S 486 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2)
--R
--R
--R   (1)
--R          4      3      2           +--------+ +------+
--R     (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R  /
--R             7         6         5         4         3        2
--R       (2187x  + 10206x  + 20412x  + 22680x  + 15120x  + 6048x  + 1344x + 128)
--R    *
--R        +------+
--R       \|3x + 2
--R                                                    Type: Expression(Integer)
--E 486
--S 487 of 500
--r0:=-2/39*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_
--     370/1287*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)-_
--     129922578224/2252673423*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)*sqrt(5/7)+18761985160/2252673423*_
--     elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_
--     2622980/1702701*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+_
--     60080/34749*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_
--     54281308/35756721*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_

--     1876198516/750891141*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     129922578224/5256237987*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 487
--S 488 of 500
--a0:=integrate(t0,x)
--E 488
--S 489 of 500
--m0:=a0-r0
--E 489
--S 490 of 500
--d0:=D(m0,x)
--E 490
)clear all
--S 491 of 500
t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(17/2)
--R
--R
--R   (1)
--R          4      3      2           +--------+ +------+
--R     (100x  + 20x  - 59x  - 6x + 9)\|- 2x + 1 \|5x + 3
--R  /
--R              8         7         6          5         4         3         2
--R         6561x  + 34992x  + 81648x  + 108864x  + 90720x  + 48384x  + 16128x
--R       +
--R         3072x + 256
--R    *
--R        +------+
--R       \|3x + 2
--R                                                    Type: Expression(Integer)
--E 491
--S 492 of 500
--r0:=-2/45*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2)+_
--     74/351*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_
--     363883755904/15768713961*elliptic_f(asin(sqrt(3/7)*_
--     sqrt(1-2*x)),35/33)/sqrt(33)-12641611554328/15768713961*_
--     elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_
--     1085156/729729*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+_
--     16636/11583*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)-_
--     112817764/107270163*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_
--     3914701972/3754455705*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_
--     181941877952/26281189935*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_
--     12641611554328/183968329545*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x)
--E 492

--S 494 of 500
--m0:=a0-r0
--E 494
--S 495 of 500
--d0:=D(m0,x)
--E 495
)clear all
--S 496 of 500
t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)/sqrt(3+5*x)
--R
--R
--R            4      3      2           +--------+ +------+
--R        (36x  + 12x  - 23x  - 4x + 4)\|- 2x + 1 \|3x + 2
--R   (1)  -------------------------------------------------
--R                             +------+
--R                            \|5x + 3
--R                                                    Type: Expression(Integer)
--E 496
--S 497 of 500
--r0:=2865161/8353125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_
--     sqrt(33)-231061879/16706250*elliptic_e(asin(sqrt(5/11)*_
--     sqrt(1-2*x)),33/35)/sqrt(35)+62/1485*(1-2*x)^(3/2)*(2+3*x)^(5/2)*_
--     sqrt(3+5*x)+2/55*(1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+_
--     181333/3898125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_
--     4258/155925*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_
--     2865161/19490625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)
--E 497
--S 498 of 500
--a0:=integrate(t0,x)
--E 498
--S 499 of 500
--m0:=a0-r0
--E 499
--S 500 of 500
--d0:=D(m0,x)
--E 500
)spool
)lisp (bye)

———- 73

References^{[1] nothing}

74