3.1436 \(\int \frac{(2+3 x)^6 (3+5 x)^2}{1-2 x} \, dx\)

Optimal. Leaf size=65 \[ -\frac{18225 x^8}{16}-\frac{207765 x^7}{28}-\frac{356643 x^6}{16}-\frac{3310281 x^5}{80}-\frac{6947721 x^4}{128}-\frac{3575427 x^3}{64}-\frac{13178761 x^2}{256}-\frac{14088073 x}{256}-\frac{14235529}{512} \log (1-2 x) \]

[Out]

(-14088073*x)/256 - (13178761*x^2)/256 - (3575427*x^3)/64 - (6947721*x^4)/128 -
(3310281*x^5)/80 - (356643*x^6)/16 - (207765*x^7)/28 - (18225*x^8)/16 - (1423552
9*Log[1 - 2*x])/512

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Rubi [A]  time = 0.0655079, 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 \[ -\frac{18225 x^8}{16}-\frac{207765 x^7}{28}-\frac{356643 x^6}{16}-\frac{3310281 x^5}{80}-\frac{6947721 x^4}{128}-\frac{3575427 x^3}{64}-\frac{13178761 x^2}{256}-\frac{14088073 x}{256}-\frac{14235529}{512} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x),x]

[Out]

(-14088073*x)/256 - (13178761*x^2)/256 - (3575427*x^3)/64 - (6947721*x^4)/128 -
(3310281*x^5)/80 - (356643*x^6)/16 - (207765*x^7)/28 - (18225*x^8)/16 - (1423552
9*Log[1 - 2*x])/512

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{18225 x^{8}}{16} - \frac{207765 x^{7}}{28} - \frac{356643 x^{6}}{16} - \frac{3310281 x^{5}}{80} - \frac{6947721 x^{4}}{128} - \frac{3575427 x^{3}}{64} - \frac{14235529 \log{\left (- 2 x + 1 \right )}}{512} + \int \left (- \frac{14088073}{256}\right )\, dx - \frac{13178761 \int x\, dx}{128} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**6*(3+5*x)**2/(1-2*x),x)

[Out]

-18225*x**8/16 - 207765*x**7/28 - 356643*x**6/16 - 3310281*x**5/80 - 6947721*x**
4/128 - 3575427*x**3/64 - 14235529*log(-2*x + 1)/512 + Integral(-14088073/256, x
) - 13178761*Integral(x, x)/128

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Mathematica [A]  time = 0.0216014, size = 52, normalized size = 0.8 \[ \frac{-163296000 x^8-1063756800 x^7-3195521280 x^6-5932023552 x^5-7781447520 x^4-8008956480 x^3-7380106160 x^2-7889320880 x-3985948120 \log (1-2 x)[phone]}{143360} \]

Antiderivative was successfully verified.

[In]  Integrate[((2 + 3*x)^6*(3 + 5*x)^2)/(1 - 2*x),x]

[Out]

(7521401241 - 7889320880*x - 7380106160*x^2 - 8008956480*x^3 - 7781447520*x^4 -
5932023552*x^5 - 3195521280*x^6 - 1063756800*x^7 - 163296000*x^8 - 3985948120*Lo
g[1 - 2*x])/143360

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Maple [A]  time = 0.004, size = 48, normalized size = 0.7 \[ -{\frac{18225\,{x}^{8}}{16}}-{\frac{207765\,{x}^{7}}{28}}-{\frac{356643\,{x}^{6}}{16}}-{\frac{3310281\,{x}^{5}}{80}}-{\frac{6947721\,{x}^{4}}{128}}-{\frac{3575427\,{x}^{3}}{64}}-{\frac{13178761\,{x}^{2}}{256}}-{\frac{14088073\,x}{256}}-{\frac{14235529\,\ln \left ( -1+2\,x \right ) }{512}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^6*(3+5*x)^2/(1-2*x),x)

[Out]

-18225/16*x^8-207765/28*x^7-356643/16*x^6-3310281/80*x^5-6947721/128*x^4-3575427
/64*x^3-13178761/256*x^2-14088073/256*x-14235529/512*ln(-1+2*x)

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Maxima [A]  time = 1.35591, size = 63, normalized size = 0.97 \[ -\frac{18225}{16} \, x^{8} - \frac{207765}{28} \, x^{7} - \frac{356643}{16} \, x^{6} - \frac{3310281}{80} \, x^{5} - \frac{6947721}{128} \, x^{4} - \frac{3575427}{64} \, x^{3} - \frac{13178761}{256} \, x^{2} - \frac{14088073}{256} \, x - \frac{14235529}{512} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(3*x + 2)^6/(2*x - 1),x, algorithm="maxima")

[Out]

-18225/16*x^8 - 207765/28*x^7 - 356643/16*x^6 - 3310281/80*x^5 - 6947721/128*x^4
- 3575427/64*x^3 - 13178761/256*x^2 - 14088073/256*x - 14235529/512*log(2*x - 1
)

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Fricas [A]  time = 0.226752, size = 63, normalized size = 0.97 \[ -\frac{18225}{16} \, x^{8} - \frac{207765}{28} \, x^{7} - \frac{356643}{16} \, x^{6} - \frac{3310281}{80} \, x^{5} - \frac{6947721}{128} \, x^{4} - \frac{3575427}{64} \, x^{3} - \frac{13178761}{256} \, x^{2} - \frac{14088073}{256} \, x - \frac{14235529}{512} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(3*x + 2)^6/(2*x - 1),x, algorithm="fricas")

[Out]

-18225/16*x^8 - 207765/28*x^7 - 356643/16*x^6 - 3310281/80*x^5 - 6947721/128*x^4
- 3575427/64*x^3 - 13178761/256*x^2 - 14088073/256*x - 14235529/512*log(2*x - 1
)

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Sympy [A]  time = 0.227874, size = 63, normalized size = 0.97 \[ - \frac{18225 x^{8}}{16} - \frac{207765 x^{7}}{28} - \frac{356643 x^{6}}{16} - \frac{3310281 x^{5}}{80} - \frac{6947721 x^{4}}{128} - \frac{3575427 x^{3}}{64} - \frac{13178761 x^{2}}{256} - \frac{14088073 x}{256} - \frac{14235529 \log{\left (2 x - 1 \right )}}{512} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**6*(3+5*x)**2/(1-2*x),x)

[Out]

-18225*x**8/16 - 207765*x**7/28 - 356643*x**6/16 - 3310281*x**5/80 - 6947721*x**
4/128 - 3575427*x**3/64 - 13178761*x**2/256 - 14088073*x/256 - 14235529*log(2*x
- 1)/512

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GIAC/XCAS [A]  time = 0.20847, size = 65, normalized size = 1. \[ -\frac{18225}{16} \, x^{8} - \frac{207765}{28} \, x^{7} - \frac{356643}{16} \, x^{6} - \frac{3310281}{80} \, x^{5} - \frac{6947721}{128} \, x^{4} - \frac{3575427}{64} \, x^{3} - \frac{13178761}{256} \, x^{2} - \frac{14088073}{256} \, x - \frac{14235529}{512} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)^2*(3*x + 2)^6/(2*x - 1),x, algorithm="giac")

[Out]

-18225/16*x^8 - 207765/28*x^7 - 356643/16*x^6 - 3310281/80*x^5 - 6947721/128*x^4
- 3575427/64*x^3 - 13178761/256*x^2 - 14088073/256*x - 14235529/512*ln(abs(2*x
- 1))