3.1682 \(\int \frac{(2+3 x)^7}{(1-2 x)^3 (3+5 x)^3} \, dx\)

Optimal. Leaf size=77 \[ -\frac{2187 x^2}{2000}-\frac{95499 x}{10000}-\frac{7411887}{234256 (1-2 x)}-\frac{237}{45753125 (5 x+3)}+\frac{823543}{85184 (1-2 x)^2}-\frac{1}{8318750 (5 x+3)^2}-\frac{25059237 \log (1-2 x)}{1288408}+\frac{24279 \log (5 x+3)}{503284375} \]

[Out]

823543/(85184*(1 - 2*x)^2) - 7411887/(234256*(1 - 2*x)) - (95499*x)/10000 - (218
7*x^2)/2000 - 1/(8318750*(3 + 5*x)^2) - 237/(45753125*(3 + 5*x)) - (25059237*Log
[1 - 2*x])/1288408 + (24279*Log[3 + 5*x])/503284375

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Rubi [A]  time = 0.0930943, antiderivative size = 77, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{2187 x^2}{2000}-\frac{95499 x}{10000}-\frac{7411887}{234256 (1-2 x)}-\frac{237}{45753125 (5 x+3)}+\frac{823543}{85184 (1-2 x)^2}-\frac{1}{8318750 (5 x+3)^2}-\frac{25059237 \log (1-2 x)}{1288408}+\frac{24279 \log (5 x+3)}{503284375} \]

Antiderivative was successfully verified.

[In]  Int[(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)^3),x]

[Out]

823543/(85184*(1 - 2*x)^2) - 7411887/(234256*(1 - 2*x)) - (95499*x)/10000 - (218
7*x^2)/2000 - 1/(8318750*(3 + 5*x)^2) - 237/(45753125*(3 + 5*x)) - (25059237*Log
[1 - 2*x])/1288408 + (24279*Log[3 + 5*x])/503284375

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{25059237 \log{\left (- 2 x + 1 \right )}}{1288408} + \frac{24279 \log{\left (5 x + 3 \right )}}{503284375} + \int \left (- \frac{95499}{10000}\right )\, dx - \frac{2187 \int x\, dx}{1000} - \frac{237}{45753125 \left (5 x + 3\right )} - \frac{1}{8318750 \left (5 x + 3\right )^{2}} - \frac{7411887}{234256 \left (- 2 x + 1\right )} + \frac{823543}{85184 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**7/(1-2*x)**3/(3+5*x)**3,x)

[Out]

-25059237*log(-2*x + 1)/1288408 + 24279*log(5*x + 3)/503284375 + Integral(-95499
/10000, x) - 2187*Integral(x, x)/1000 - 237/(45753125*(5*x + 3)) - 1/(8318750*(5
*x + 3)**2) - 7411887/(234256*(-2*x + 1)) + 823543/(85184*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0638939, size = 65, normalized size = 0.84 \[ \frac{-\frac{11 \left (320198670000 x^6+2860441452000 x^5+2092320420300 x^4-5957126547060 x^3-5105353973121 x^2+410862940766 x+734029874011\right )}{\left (10 x^2+x-3\right )^2}-626480925000 \log (3-6 x)+1553856 \log (-3 (5 x+3))}{32210200000} \]

Antiderivative was successfully verified.

[In]  Integrate[(2 + 3*x)^7/((1 - 2*x)^3*(3 + 5*x)^3),x]

[Out]

((-11*(734029874011 + 410862940766*x - 5105353973121*x^2 - 5957126547060*x^3 + 2
092320420300*x^4 + 2860441452000*x^5 + 320198670000*x^6))/(-3 + x + 10*x^2)^2 -
626480925000*Log[3 - 6*x] + 1553856*Log[-3*(3 + 5*x)])/32210200000

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Maple [A]  time = 0.015, size = 62, normalized size = 0.8 \[ -{\frac{2187\,{x}^{2}}{2000}}-{\frac{95499\,x}{10000}}-{\frac{1}{8318750\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{237}{137259375+228765625\,x}}+{\frac{24279\,\ln \left ( 3+5\,x \right ) }{503284375}}+{\frac{823543}{85184\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{7411887}{-234256+468512\,x}}-{\frac{25059237\,\ln \left ( -1+2\,x \right ) }{1288408}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^7/(1-2*x)^3/(3+5*x)^3,x)

[Out]

-2187/2000*x^2-95499/10000*x-1/8318750/(3+5*x)^2-237/45753125/(3+5*x)+24279/5032
84375*ln(3+5*x)+823543/85184/(-1+2*x)^2+7411887/234256/(-1+2*x)-25059237/1288408
*ln(-1+2*x)

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Maxima [A]  time = 1.35179, size = 86, normalized size = 1.12 \[ -\frac{2187}{2000} \, x^{2} - \frac{95499}{10000} \, x + \frac{4632429071640 \, x^{3} + 3950432948061 \, x^{2} - 262504223666 \, x - 579053717731}{2928200000 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{24279}{503284375} \, \log \left (5 \, x + 3\right ) - \frac{25059237}{1288408} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^7/((5*x + 3)^3*(2*x - 1)^3),x, algorithm="maxima")

[Out]

-2187/2000*x^2 - 95499/10000*x + 1/2928200000*(4632429071640*x^3 + 3950432948061
*x^2 - 262504223666*x - 579053717731)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9) + 24
279/503284375*log(5*x + 3) - 25059237/1288408*log(2*x - 1)

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Fricas [A]  time = 0.212516, size = 149, normalized size = 1.94 \[ -\frac{3522185370000 \, x^{6} + 31464855972000 \, x^{5} + 4073994411300 \, x^{4} - 69316698060060 \, x^{3} - 44983390879251 \, x^{2} - 1553856 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 626480925000 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) + 5655984161146 \, x + 6369590895041}{32210200000 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^7/((5*x + 3)^3*(2*x - 1)^3),x, algorithm="fricas")

[Out]

-1/32210200000*(3522185370000*x^6 + 31464855972000*x^5 + 4073994411300*x^4 - 693
16698060060*x^3 - 44983390879251*x^2 - 1553856*(100*x^4 + 20*x^3 - 59*x^2 - 6*x
+ 9)*log(5*x + 3) + 626480925000*(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)*log(2*x -
1) + 5655984161146*x + 6369590895041)/(100*x^4 + 20*x^3 - 59*x^2 - 6*x + 9)

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Sympy [A]  time = 0.575552, size = 66, normalized size = 0.86 \[ - \frac{2187 x^{2}}{2000} - \frac{95499 x}{10000} + \frac{4632429071640 x^{3} + 3950432948061 x^{2} - 262504223666 x - 579053717731}{292820000000 x^{4} + 58564000000 x^{3} - 172763800000 x^{2} - 17569200000 x + 26353800000} - \frac{25059237 \log{\left (x - \frac{1}{2} \right )}}{1288408} + \frac{24279 \log{\left (x + \frac{3}{5} \right )}}{503284375} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**7/(1-2*x)**3/(3+5*x)**3,x)

[Out]

-2187*x**2/2000 - 95499*x/10000 + (4632429071640*x**3 + 3950432948061*x**2 - 262
504223666*x - 579053717731)/(292820000000*x**4 + 58564000000*x**3 - 172763800000
*x**2 - 17569200000*x + 26353800000) - 25059237*log(x - 1/2)/1288408 + 24279*log
(x + 3/5)/503284375

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GIAC/XCAS [A]  time = 0.212058, size = 78, normalized size = 1.01 \[ -\frac{2187}{2000} \, x^{2} - \frac{95499}{10000} \, x + \frac{4632429071640 \, x^{3} + 3950432948061 \, x^{2} - 262504223666 \, x - 579053717731}{2928200000 \,{\left (5 \, x + 3\right )}^{2}{\left (2 \, x - 1\right )}^{2}} + \frac{24279}{503284375} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{25059237}{1288408} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(3*x + 2)^7/((5*x + 3)^3*(2*x - 1)^3),x, algorithm="giac")

[Out]

-2187/2000*x^2 - 95499/10000*x + 1/2928200000*(4632429071640*x^3 + 3950432948061
*x^2 - 262504223666*x - 579053717731)/((5*x + 3)^2*(2*x - 1)^2) + 24279/50328437
5*ln(abs(5*x + 3)) - 25059237/1288408*ln(abs(2*x - 1))