3.1559 \(\int \frac{(2+3 x)^3 (3+5 x)^3}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=55 \[ \frac{675 x^5}{4}+\frac{2025 x^4}{2}+\frac{47535 x^3}{16}+\frac{194881 x^2}{32}+\frac{766807 x}{64}+\frac{456533}{128 (1-2 x)}+\frac{302379}{32} \log (1-2 x) \]

[Out]

456533/(128*(1 - 2*x)) + (766807*x)/64 + (194881*x^2)/32 + (47535*x^3)/16 + (202
5*x^4)/2 + (675*x^5)/4 + (302379*Log[1 - 2*x])/32

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Rubi [A]  time = 0.0721014, antiderivative size = 55, 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 \[ \frac{675 x^5}{4}+\frac{2025 x^4}{2}+\frac{47535 x^3}{16}+\frac{194881 x^2}{32}+\frac{766807 x}{64}+\frac{456533}{128 (1-2 x)}+\frac{302379}{32} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

456533/(128*(1 - 2*x)) + (766807*x)/64 + (194881*x^2)/32 + (47535*x^3)/16 + (202
5*x^4)/2 + (675*x^5)/4 + (302379*Log[1 - 2*x])/32

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{675 x^{5}}{4} + \frac{2025 x^{4}}{2} + \frac{47535 x^{3}}{16} + \frac{302379 \log{\left (- 2 x + 1 \right )}}{32} + \int \frac{766807}{64}\, dx + \frac{194881 \int x\, dx}{16} + \frac{456533}{128 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675*x**5/4 + 2025*x**4/2 + 47535*x**3/16 + 302379*log(-2*x + 1)/32 + Integral(76
6807/64, x) + 194881*Integral(x, x)/16 + 456533/(128*(-2*x + 1))

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Mathematica [A]  time = 0.0229457, size = 54, normalized size = 0.98 \[ \frac{43200 x^6+237600 x^5+630960 x^4+1178768 x^3+2287704 x^2-3569610 x+1209516 (2 x-1) \log (1-2 x)+561465}{128 (2 x-1)} \]

Antiderivative was successfully verified.

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

[Out]

(561465 - 3569610*x + 2287704*x^2 + 1178768*x^3 + 630960*x^4 + 237600*x^5 + 4320
0*x^6 + 1209516*(-1 + 2*x)*Log[1 - 2*x])/(128*(-1 + 2*x))

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Maple [A]  time = 0.008, size = 42, normalized size = 0.8 \[{\frac{675\,{x}^{5}}{4}}+{\frac{2025\,{x}^{4}}{2}}+{\frac{47535\,{x}^{3}}{16}}+{\frac{194881\,{x}^{2}}{32}}+{\frac{766807\,x}{64}}-{\frac{456533}{-128+256\,x}}+{\frac{302379\,\ln \left ( -1+2\,x \right ) }{32}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/4*x^5+2025/2*x^4+47535/16*x^3+194881/32*x^2+766807/64*x-456533/128/(-1+2*x)+
302379/32*ln(-1+2*x)

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Maxima [A]  time = 1.34773, size = 55, normalized size = 1. \[ \frac{675}{4} \, x^{5} + \frac{2025}{2} \, x^{4} + \frac{47535}{16} \, x^{3} + \frac{194881}{32} \, x^{2} + \frac{766807}{64} \, x - \frac{456533}{128 \,{\left (2 \, x - 1\right )}} + \frac{302379}{32} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675/4*x^5 + 2025/2*x^4 + 47535/16*x^3 + 194881/32*x^2 + 766807/64*x - 456533/128
/(2*x - 1) + 302379/32*log(2*x - 1)

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Fricas [A]  time = 0.203421, size = 70, normalized size = 1.27 \[ \frac{43200 \, x^{6} + 237600 \, x^{5} + 630960 \, x^{4} + 1178768 \, x^{3} + 2287704 \, x^{2} + 1209516 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 1533614 \, x - 456533}{128 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/128*(43200*x^6 + 237600*x^5 + 630960*x^4 + 1178768*x^3 + 2287704*x^2 + 1209516
*(2*x - 1)*log(2*x - 1) - 1533614*x - 456533)/(2*x - 1)

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Sympy [A]  time = 0.225566, size = 48, normalized size = 0.87 \[ \frac{675 x^{5}}{4} + \frac{2025 x^{4}}{2} + \frac{47535 x^{3}}{16} + \frac{194881 x^{2}}{32} + \frac{766807 x}{64} + \frac{302379 \log{\left (2 x - 1 \right )}}{32} - \frac{456533}{256 x - 128} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

675*x**5/4 + 2025*x**4/2 + 47535*x**3/16 + 194881*x**2/32 + 766807*x/64 + 302379
*log(2*x - 1)/32 - 456533/(256*x - 128)

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GIAC/XCAS [A]  time = 0.21229, size = 101, normalized size = 1.84 \[ \frac{1}{128} \,{\left (2 \, x - 1\right )}^{5}{\left (\frac{11475}{2 \, x - 1} + \frac{86685}{{\left (2 \, x - 1\right )}^{2}} + \frac{392836}{{\left (2 \, x - 1\right )}^{3}} + \frac{1334949}{{\left (2 \, x - 1\right )}^{4}} + 675\right )} - \frac{456533}{128 \,{\left (2 \, x - 1\right )}} - \frac{302379}{32} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/128*(2*x - 1)^5*(11475/(2*x - 1) + 86685/(2*x - 1)^2 + 392836/(2*x - 1)^3 + 13
34949/(2*x - 1)^4 + 675) - 456533/128/(2*x - 1) - 302379/32*ln(1/2*abs(2*x - 1)/
(2*x - 1)^2)