3.1453 \(\int \frac{(2+3 x)^5 (3+5 x)^3}{1-2 x} \, dx\)

Optimal. Leaf size=65 \[ -\frac{30375 x^8}{16}-\frac{342225 x^7}{28}-\frac{580815 x^6}{16}-\frac{5333733 x^5}{80}-\frac{11088453 x^4}{128}-\frac{16987973 x^3}{192}-\frac{20766533 x^2}{256}-\frac{22148933 x}{256}-\frac{22370117}{512} \log (1-2 x) \]

[Out]

(-22148933*x)/256 - (20766533*x^2)/256 - (16987973*x^3)/192 - (11088453*x^4)/128
- (5333733*x^5)/80 - (580815*x^6)/16 - (342225*x^7)/28 - (30375*x^8)/16 - (2237
0117*Log[1 - 2*x])/512

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Rubi [A]  time = 0.0676214, antiderivative size = 65, 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 \[ -\frac{30375 x^8}{16}-\frac{342225 x^7}{28}-\frac{580815 x^6}{16}-\frac{5333733 x^5}{80}-\frac{11088453 x^4}{128}-\frac{16987973 x^3}{192}-\frac{20766533 x^2}{256}-\frac{22148933 x}{256}-\frac{22370117}{512} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

(-22148933*x)/256 - (20766533*x^2)/256 - (16987973*x^3)/192 - (11088453*x^4)/128
- (5333733*x^5)/80 - (580815*x^6)/16 - (342225*x^7)/28 - (30375*x^8)/16 - (2237
0117*Log[1 - 2*x])/512

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{30375 x^{8}}{16} - \frac{342225 x^{7}}{28} - \frac{580815 x^{6}}{16} - \frac{5333733 x^{5}}{80} - \frac{11088453 x^{4}}{128} - \frac{16987973 x^{3}}{192} - \frac{22370117 \log{\left (- 2 x + 1 \right )}}{512} + \int \left (- \frac{22148933}{256}\right )\, dx - \frac{20766533 \int x\, dx}{128} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30375*x**8/16 - 342225*x**7/28 - 580815*x**6/16 - 5333733*x**5/80 - 11088453*x*
*4/128 - 16987973*x**3/192 - 22370117*log(-2*x + 1)/512 + Integral(-22148933/256
, x) - 20766533*Integral(x, x)/128

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Mathematica [A]  time = 0.0210101, size = 68, normalized size = 1.05 \[ -\frac{30375 x^8}{16}-\frac{342225 x^7}{28}-\frac{580815 x^6}{16}-\frac{5333733 x^5}{80}-\frac{11088453 x^4}{128}-\frac{16987973 x^3}{192}-\frac{20766533 x^2}{256}-\frac{22148933 x}{256}-\frac{22370117}{512} \log (1-2 x)+\frac{35596520969}{430080} \]

Antiderivative was successfully verified.

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

[Out]

35596520969/430080 - (22148933*x)/256 - (20766533*x^2)/256 - (16987973*x^3)/192
- (11088453*x^4)/128 - (5333733*x^5)/80 - (580815*x^6)/16 - (342225*x^7)/28 - (3
0375*x^8)/16 - (22370117*Log[1 - 2*x])/512

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Maple [A]  time = 0.004, size = 48, normalized size = 0.7 \[ -{\frac{30375\,{x}^{8}}{16}}-{\frac{342225\,{x}^{7}}{28}}-{\frac{580815\,{x}^{6}}{16}}-{\frac{5333733\,{x}^{5}}{80}}-{\frac{11088453\,{x}^{4}}{128}}-{\frac{16987973\,{x}^{3}}{192}}-{\frac{20766533\,{x}^{2}}{256}}-{\frac{22148933\,x}{256}}-{\frac{22370117\,\ln \left ( -1+2\,x \right ) }{512}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30375/16*x^8-342225/28*x^7-580815/16*x^6-5333733/80*x^5-11088453/128*x^4-169879
73/192*x^3-20766533/256*x^2-22148933/256*x-22370117/512*ln(-1+2*x)

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Maxima [A]  time = 1.3435, size = 63, normalized size = 0.97 \[ -\frac{30375}{16} \, x^{8} - \frac{342225}{28} \, x^{7} - \frac{580815}{16} \, x^{6} - \frac{5333733}{80} \, x^{5} - \frac{11088453}{128} \, x^{4} - \frac{16987973}{192} \, x^{3} - \frac{20766533}{256} \, x^{2} - \frac{22148933}{256} \, x - \frac{22370117}{512} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30375/16*x^8 - 342225/28*x^7 - 580815/16*x^6 - 5333733/80*x^5 - 11088453/128*x^
4 - 16987973/192*x^3 - 20766533/256*x^2 - 22148933/256*x - 22370117/512*log(2*x
- 1)

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Fricas [A]  time = 0.224039, size = 63, normalized size = 0.97 \[ -\frac{30375}{16} \, x^{8} - \frac{342225}{28} \, x^{7} - \frac{580815}{16} \, x^{6} - \frac{5333733}{80} \, x^{5} - \frac{11088453}{128} \, x^{4} - \frac{16987973}{192} \, x^{3} - \frac{20766533}{256} \, x^{2} - \frac{22148933}{256} \, x - \frac{22370117}{512} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30375/16*x^8 - 342225/28*x^7 - 580815/16*x^6 - 5333733/80*x^5 - 11088453/128*x^
4 - 16987973/192*x^3 - 20766533/256*x^2 - 22148933/256*x - 22370117/512*log(2*x
- 1)

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Sympy [A]  time = 0.224922, size = 63, normalized size = 0.97 \[ - \frac{30375 x^{8}}{16} - \frac{342225 x^{7}}{28} - \frac{580815 x^{6}}{16} - \frac{5333733 x^{5}}{80} - \frac{11088453 x^{4}}{128} - \frac{16987973 x^{3}}{192} - \frac{20766533 x^{2}}{256} - \frac{22148933 x}{256} - \frac{22370117 \log{\left (2 x - 1 \right )}}{512} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30375*x**8/16 - 342225*x**7/28 - 580815*x**6/16 - 5333733*x**5/80 - 11088453*x*
*4/128 - 16987973*x**3/192 - 20766533*x**2/256 - 22148933*x/256 - 22370117*log(2
*x - 1)/512

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GIAC/XCAS [A]  time = 0.209537, size = 65, normalized size = 1. \[ -\frac{30375}{16} \, x^{8} - \frac{342225}{28} \, x^{7} - \frac{580815}{16} \, x^{6} - \frac{5333733}{80} \, x^{5} - \frac{11088453}{128} \, x^{4} - \frac{16987973}{192} \, x^{3} - \frac{20766533}{256} \, x^{2} - \frac{22148933}{256} \, x - \frac{22370117}{512} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-30375/16*x^8 - 342225/28*x^7 - 580815/16*x^6 - 5333733/80*x^5 - 11088453/128*x^
4 - 16987973/192*x^3 - 20766533/256*x^2 - 22148933/256*x - 22370117/512*ln(abs(2
*x - 1))