3.1646 \(\int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=52 \[ -\frac{375 x^3}{8}-\frac{10425 x^2}{32}-\frac{5695 x}{4}-\frac{144837}{64 (1-2 x)}+\frac{65219}{128 (1-2 x)^2}-\frac{64317}{32} \log (1-2 x) \]

[Out]

65219/(128*(1 - 2*x)^2) - 144837/(64*(1 - 2*x)) - (5695*x)/4 - (10425*x^2)/32 -
(375*x^3)/8 - (64317*Log[1 - 2*x])/32

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Rubi [A]  time = 0.0727549, antiderivative size = 52, 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 \[ -\frac{375 x^3}{8}-\frac{10425 x^2}{32}-\frac{5695 x}{4}-\frac{144837}{64 (1-2 x)}+\frac{65219}{128 (1-2 x)^2}-\frac{64317}{32} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

65219/(128*(1 - 2*x)^2) - 144837/(64*(1 - 2*x)) - (5695*x)/4 - (10425*x^2)/32 -
(375*x^3)/8 - (64317*Log[1 - 2*x])/32

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{375 x^{3}}{8} - \frac{64317 \log{\left (- 2 x + 1 \right )}}{32} + \int \left (- \frac{5695}{4}\right )\, dx - \frac{10425 \int x\, dx}{16} - \frac{144837}{64 \left (- 2 x + 1\right )} + \frac{65219}{128 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x**3/8 - 64317*log(-2*x + 1)/32 + Integral(-5695/4, x) - 10425*Integral(x,
x)/16 - 144837/(64*(-2*x + 1)) + 65219/(128*(-2*x + 1)**2)

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Mathematica [A]  time = 0.0327042, size = 47, normalized size = 0.9 \[ \frac{1}{32} \left (-\frac{2 \left (3000 x^5+17850 x^4+71020 x^3-137055 x^2+1509 x+15270\right )}{(1-2 x)^2}-64317 \log (1-2 x)\right ) \]

Antiderivative was successfully verified.

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

[Out]

((-2*(15270 + 1509*x - 137055*x^2 + 71020*x^3 + 17850*x^4 + 3000*x^5))/(1 - 2*x)
^2 - 64317*Log[1 - 2*x])/32

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Maple [A]  time = 0.01, size = 41, normalized size = 0.8 \[ -{\frac{375\,{x}^{3}}{8}}-{\frac{10425\,{x}^{2}}{32}}-{\frac{5695\,x}{4}}+{\frac{65219}{128\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{144837}{-64+128\,x}}-{\frac{64317\,\ln \left ( -1+2\,x \right ) }{32}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/8*x^3-10425/32*x^2-5695/4*x+65219/128/(-1+2*x)^2+144837/64/(-1+2*x)-64317/3
2*ln(-1+2*x)

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Maxima [A]  time = 1.3556, size = 55, normalized size = 1.06 \[ -\frac{375}{8} \, x^{3} - \frac{10425}{32} \, x^{2} - \frac{5695}{4} \, x + \frac{847 \,{\left (684 \, x - 265\right )}}{128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{64317}{32} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/8*x^3 - 10425/32*x^2 - 5695/4*x + 847/128*(684*x - 265)/(4*x^2 - 4*x + 1) -
64317/32*log(2*x - 1)

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Fricas [A]  time = 0.214548, size = 77, normalized size = 1.48 \[ -\frac{24000 \, x^{5} + 142800 \, x^{4} + 568160 \, x^{3} - 687260 \, x^{2} + 257268 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 397108 \, x + 224455}{128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/128*(24000*x^5 + 142800*x^4 + 568160*x^3 - 687260*x^2 + 257268*(4*x^2 - 4*x +
1)*log(2*x - 1) - 397108*x + 224455)/(4*x^2 - 4*x + 1)

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Sympy [A]  time = 0.295771, size = 42, normalized size = 0.81 \[ - \frac{375 x^{3}}{8} - \frac{10425 x^{2}}{32} - \frac{5695 x}{4} + \frac{579348 x - 224455}{512 x^{2} - 512 x + 128} - \frac{64317 \log{\left (2 x - 1 \right )}}{32} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375*x**3/8 - 10425*x**2/32 - 5695*x/4 + (579348*x - 224455)/(512*x**2 - 512*x +
128) - 64317*log(2*x - 1)/32

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GIAC/XCAS [A]  time = 0.213739, size = 50, normalized size = 0.96 \[ -\frac{375}{8} \, x^{3} - \frac{10425}{32} \, x^{2} - \frac{5695}{4} \, x + \frac{847 \,{\left (684 \, x - 265\right )}}{128 \,{\left (2 \, x - 1\right )}^{2}} - \frac{64317}{32} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-375/8*x^3 - 10425/32*x^2 - 5695/4*x + 847/128*(684*x - 265)/(2*x - 1)^2 - 64317
/32*ln(abs(2*x - 1))