3.1435 \(\int \frac{(2+3 x)^7 (3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=72 \[ -\frac{6075 x^9}{2}-\frac{696195 x^8}{32}-\frac{4040847 x^7}{56}-\frac{4736853 x^6}{32}-\frac{34084287 x^5}{160}-\frac{59969727 x^4}{256}-\frac{27480469 x^3}{128}-\frac{94979263 x^2}{512}-\frac{99058879 x}{512}-\frac{99648703 \log (1-2 x)}{1024} \]

[Out]

(-99058879*x)/512 - (94979263*x^2)/512 - (27480469*x^3)/128 - (59969727*x^4)/256
- (34084287*x^5)/160 - (4736853*x^6)/32 - (4040847*x^7)/56 - (696195*x^8)/32 -
(6075*x^9)/2 - (99648703*Log[1 - 2*x])/1024

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Rubi [A]  time = 0.0711837, antiderivative size = 72, 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 \[ -\frac{6075 x^9}{2}-\frac{696195 x^8}{32}-\frac{4040847 x^7}{56}-\frac{4736853 x^6}{32}-\frac{34084287 x^5}{160}-\frac{59969727 x^4}{256}-\frac{27480469 x^3}{128}-\frac{94979263 x^2}{512}-\frac{99058879 x}{512}-\frac{99648703 \log (1-2 x)}{1024} \]

Antiderivative was successfully verified.

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

[Out]

(-99058879*x)/512 - (94979263*x^2)/512 - (27480469*x^3)/128 - (59969727*x^4)/256
- (34084287*x^5)/160 - (4736853*x^6)/32 - (4040847*x^7)/56 - (696195*x^8)/32 -
(6075*x^9)/2 - (99648703*Log[1 - 2*x])/1024

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{6075 x^{9}}{2} - \frac{696195 x^{8}}{32} - \frac{4040847 x^{7}}{56} - \frac{4736853 x^{6}}{32} - \frac{34084287 x^{5}}{160} - \frac{59969727 x^{4}}{256} - \frac{27480469 x^{3}}{128} - \frac{99648703 \log{\left (- 2 x + 1 \right )}}{1024} + \int \left (- \frac{99058879}{512}\right )\, dx - \frac{94979263 \int x\, dx}{256} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075*x**9/2 - 696195*x**8/32 - 4040847*x**7/56 - 4736853*x**6/32 - 34084287*x**
5/160 - 59969727*x**4/256 - 27480469*x**3/128 - 99648703*log(-2*x + 1)/1024 + In
tegral(-99058879/512, x) - 94979263*Integral(x, x)/256

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Mathematica [A]  time = 0.022713, size = 75, normalized size = 1.04 \[ -\frac{6075 x^9}{2}-\frac{696195 x^8}{32}-\frac{4040847 x^7}{56}-\frac{4736853 x^6}{32}-\frac{34084287 x^5}{160}-\frac{59969727 x^4}{256}-\frac{27480469 x^3}{128}-\frac{94979263 x^2}{512}-\frac{99058879 x}{512}-\frac{99648703 \log (1-2 x)}{1024}+\frac{55685576347}{286720} \]

Antiderivative was successfully verified.

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

[Out]

55685576347/286720 - (99058879*x)/512 - (94979263*x^2)/512 - (27480469*x^3)/128
- (59969727*x^4)/256 - (34084287*x^5)/160 - (4736853*x^6)/32 - (4040847*x^7)/56
- (696195*x^8)/32 - (6075*x^9)/2 - (99648703*Log[1 - 2*x])/1024

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Maple [A]  time = 0.005, size = 53, normalized size = 0.7 \[ -{\frac{6075\,{x}^{9}}{2}}-{\frac{696195\,{x}^{8}}{32}}-{\frac{4040847\,{x}^{7}}{56}}-{\frac{4736853\,{x}^{6}}{32}}-{\frac{34084287\,{x}^{5}}{160}}-{\frac{59969727\,{x}^{4}}{256}}-{\frac{27480469\,{x}^{3}}{128}}-{\frac{94979263\,{x}^{2}}{512}}-{\frac{99058879\,x}{512}}-{\frac{99648703\,\ln \left ( -1+2\,x \right ) }{1024}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075/2*x^9-696195/32*x^8-4040847/56*x^7-4736853/32*x^6-34084287/160*x^5-5996972
7/256*x^4-27480469/128*x^3-94979263/512*x^2-99058879/512*x-99648703/1024*ln(-1+2
*x)

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Maxima [A]  time = 1.35077, size = 70, normalized size = 0.97 \[ -\frac{6075}{2} \, x^{9} - \frac{696195}{32} \, x^{8} - \frac{4040847}{56} \, x^{7} - \frac{4736853}{32} \, x^{6} - \frac{34084287}{160} \, x^{5} - \frac{59969727}{256} \, x^{4} - \frac{27480469}{128} \, x^{3} - \frac{94979263}{512} \, x^{2} - \frac{99058879}{512} \, x - \frac{99648703}{1024} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075/2*x^9 - 696195/32*x^8 - 4040847/56*x^7 - 4736853/32*x^6 - 34084287/160*x^5
- 59969727/256*x^4 - 27480469/128*x^3 - 94979263/512*x^2 - 99058879/512*x - 996
48703/1024*log(2*x - 1)

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Fricas [A]  time = 0.238293, size = 70, normalized size = 0.97 \[ -\frac{6075}{2} \, x^{9} - \frac{696195}{32} \, x^{8} - \frac{4040847}{56} \, x^{7} - \frac{4736853}{32} \, x^{6} - \frac{34084287}{160} \, x^{5} - \frac{59969727}{256} \, x^{4} - \frac{27480469}{128} \, x^{3} - \frac{94979263}{512} \, x^{2} - \frac{99058879}{512} \, x - \frac{99648703}{1024} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075/2*x^9 - 696195/32*x^8 - 4040847/56*x^7 - 4736853/32*x^6 - 34084287/160*x^5
- 59969727/256*x^4 - 27480469/128*x^3 - 94979263/512*x^2 - 99058879/512*x - 996
48703/1024*log(2*x - 1)

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Sympy [A]  time = 0.239222, size = 70, normalized size = 0.97 \[ - \frac{6075 x^{9}}{2} - \frac{696195 x^{8}}{32} - \frac{4040847 x^{7}}{56} - \frac{4736853 x^{6}}{32} - \frac{34084287 x^{5}}{160} - \frac{59969727 x^{4}}{256} - \frac{27480469 x^{3}}{128} - \frac{94979263 x^{2}}{512} - \frac{99058879 x}{512} - \frac{99648703 \log{\left (2 x - 1 \right )}}{1024} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075*x**9/2 - 696195*x**8/32 - 4040847*x**7/56 - 4736853*x**6/32 - 34084287*x**
5/160 - 59969727*x**4/256 - 27480469*x**3/128 - 94979263*x**2/512 - 99058879*x/5
12 - 99648703*log(2*x - 1)/1024

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GIAC/XCAS [A]  time = 0.20953, size = 72, normalized size = 1. \[ -\frac{6075}{2} \, x^{9} - \frac{696195}{32} \, x^{8} - \frac{4040847}{56} \, x^{7} - \frac{4736853}{32} \, x^{6} - \frac{34084287}{160} \, x^{5} - \frac{59969727}{256} \, x^{4} - \frac{27480469}{128} \, x^{3} - \frac{94979263}{512} \, x^{2} - \frac{99058879}{512} \, x - \frac{99648703}{1024} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-6075/2*x^9 - 696195/32*x^8 - 4040847/56*x^7 - 4736853/32*x^6 - 34084287/160*x^5
- 59969727/256*x^4 - 27480469/128*x^3 - 94979263/512*x^2 - 99058879/512*x - 996
48703/1024*ln(abs(2*x - 1))