3.1645 \(\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=59 \[ -\frac{3375 x^4}{32}-\frac{11925 x^3}{16}-\frac{44595 x^2}{16}-\frac{284071 x}{32}-\frac{302379}{32 (1-2 x)}+\frac{456533}{256 (1-2 x)^2}-\frac{1334949}{128} \log (1-2 x) \]

[Out]

456533/(256*(1 - 2*x)^2) - 302379/(32*(1 - 2*x)) - (284071*x)/32 - (44595*x^2)/1
6 - (11925*x^3)/16 - (3375*x^4)/32 - (1334949*Log[1 - 2*x])/128

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Rubi [A]  time = 0.080662, antiderivative size = 59, 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 \[ -\frac{3375 x^4}{32}-\frac{11925 x^3}{16}-\frac{44595 x^2}{16}-\frac{284071 x}{32}-\frac{302379}{32 (1-2 x)}+\frac{456533}{256 (1-2 x)^2}-\frac{1334949}{128} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

456533/(256*(1 - 2*x)^2) - 302379/(32*(1 - 2*x)) - (284071*x)/32 - (44595*x^2)/1
6 - (11925*x^3)/16 - (3375*x^4)/32 - (1334949*Log[1 - 2*x])/128

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{3375 x^{4}}{32} - \frac{11925 x^{3}}{16} - \frac{1334949 \log{\left (- 2 x + 1 \right )}}{128} + \int \left (- \frac{284071}{32}\right )\, dx - \frac{44595 \int x\, dx}{8} - \frac{302379}{32 \left (- 2 x + 1\right )} + \frac{456533}{256 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375*x**4/32 - 11925*x**3/16 - 1334949*log(-2*x + 1)/128 + Integral(-284071/32,
x) - 44595*Integral(x, x)/8 - 302379/(32*(-2*x + 1)) + 456533/(256*(-2*x + 1)**
2)

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Mathematica [A]  time = 0.0314607, size = 56, normalized size = 0.95 \[ -\frac{216000 x^6+1310400 x^5+4235760 x^4+12853984 x^3-27475116 x^2+5590620 x+5339796 (1-2 x)^2 \log (1-2 x)+1244595}{512 (1-2 x)^2} \]

Antiderivative was successfully verified.

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

[Out]

-(1244595 + 5590620*x - 27475116*x^2 + 12853984*x^3 + 4235760*x^4 + 1310400*x^5
+ 216000*x^6 + 5339796*(1 - 2*x)^2*Log[1 - 2*x])/(512*(1 - 2*x)^2)

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Maple [A]  time = 0.01, size = 46, normalized size = 0.8 \[ -{\frac{3375\,{x}^{4}}{32}}-{\frac{11925\,{x}^{3}}{16}}-{\frac{44595\,{x}^{2}}{16}}-{\frac{284071\,x}{32}}+{\frac{456533}{256\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{302379}{-32+64\,x}}-{\frac{1334949\,\ln \left ( -1+2\,x \right ) }{128}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375/32*x^4-11925/16*x^3-44595/16*x^2-284071/32*x+456533/256/(-1+2*x)^2+302379/
32/(-1+2*x)-1334949/128*ln(-1+2*x)

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Maxima [A]  time = 1.36474, size = 62, normalized size = 1.05 \[ -\frac{3375}{32} \, x^{4} - \frac{11925}{16} \, x^{3} - \frac{44595}{16} \, x^{2} - \frac{284071}{32} \, x + \frac{5929 \,{\left (816 \, x - 331\right )}}{256 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{1334949}{128} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375/32*x^4 - 11925/16*x^3 - 44595/16*x^2 - 284071/32*x + 5929/256*(816*x - 331
)/(4*x^2 - 4*x + 1) - 1334949/128*log(2*x - 1)

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Fricas [A]  time = 0.211214, size = 84, normalized size = 1.42 \[ -\frac{108000 \, x^{6} + 655200 \, x^{5} + 2117880 \, x^{4} + 6426992 \, x^{3} - 8376752 \, x^{2} + 2669898 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 2565496 \, x + 1962499}{256 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/256*(108000*x^6 + 655200*x^5 + 2117880*x^4 + 6426992*x^3 - 8376752*x^2 + 2669
898*(4*x^2 - 4*x + 1)*log(2*x - 1) - 2565496*x + 1962499)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.309506, size = 49, normalized size = 0.83 \[ - \frac{3375 x^{4}}{32} - \frac{11925 x^{3}}{16} - \frac{44595 x^{2}}{16} - \frac{284071 x}{32} + \frac{4838064 x - 1962499}{1024 x^{2} - 1024 x + 256} - \frac{1334949 \log{\left (2 x - 1 \right )}}{128} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375*x**4/32 - 11925*x**3/16 - 44595*x**2/16 - 284071*x/32 + (4838064*x - 19624
99)/(1024*x**2 - 1024*x + 256) - 1334949*log(2*x - 1)/128

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GIAC/XCAS [A]  time = 0.212079, size = 57, normalized size = 0.97 \[ -\frac{3375}{32} \, x^{4} - \frac{11925}{16} \, x^{3} - \frac{44595}{16} \, x^{2} - \frac{284071}{32} \, x + \frac{5929 \,{\left (816 \, x - 331\right )}}{256 \,{\left (2 \, x - 1\right )}^{2}} - \frac{1334949}{128} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-3375/32*x^4 - 11925/16*x^3 - 44595/16*x^2 - 284071/32*x + 5929/256*(816*x - 331
)/(2*x - 1)^2 - 1334949/128*ln(abs(2*x - 1))