3.1619 \(\int \frac{(2+3 x)^2 (3+5 x)}{(1-2 x)^3} \, dx\)

Optimal. Leaf size=38 \[ -\frac{45 x}{8}-\frac{707}{16 (1-2 x)}+\frac{539}{32 (1-2 x)^2}-\frac{309}{16} \log (1-2 x) \]

[Out]

539/(32*(1 - 2*x)^2) - 707/(16*(1 - 2*x)) - (45*x)/8 - (309*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0496505, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{45 x}{8}-\frac{707}{16 (1-2 x)}+\frac{539}{32 (1-2 x)^2}-\frac{309}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

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

[Out]

539/(32*(1 - 2*x)^2) - 707/(16*(1 - 2*x)) - (45*x)/8 - (309*Log[1 - 2*x])/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{309 \log{\left (- 2 x + 1 \right )}}{16} + \int \left (- \frac{45}{8}\right )\, dx - \frac{707}{16 \left (- 2 x + 1\right )} + \frac{539}{32 \left (- 2 x + 1\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-309*log(-2*x + 1)/16 + Integral(-45/8, x) - 707/(16*(-2*x + 1)) + 539/(32*(-2*x
+ 1)**2)

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Mathematica [A]  time = 0.0376137, size = 34, normalized size = 0.89 \[ \frac{1}{32} \left (\frac{360 x^2+2468 x-785}{(1-2 x)^2}-180 x-618 \log (1-2 x)\right ) \]

Antiderivative was successfully verified.

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

[Out]

(-180*x + (-785 + 2468*x + 360*x^2)/(1 - 2*x)^2 - 618*Log[1 - 2*x])/32

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Maple [A]  time = 0.01, size = 31, normalized size = 0.8 \[ -{\frac{45\,x}{8}}+{\frac{539}{32\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{707}{-16+32\,x}}-{\frac{309\,\ln \left ( -1+2\,x \right ) }{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-45/8*x+539/32/(-1+2*x)^2+707/16/(-1+2*x)-309/16*ln(-1+2*x)

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Maxima [A]  time = 1.36422, size = 42, normalized size = 1.11 \[ -\frac{45}{8} \, x + \frac{7 \,{\left (404 \, x - 125\right )}}{32 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{309}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-45/8*x + 7/32*(404*x - 125)/(4*x^2 - 4*x + 1) - 309/16*log(2*x - 1)

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Fricas [A]  time = 0.216432, size = 63, normalized size = 1.66 \[ -\frac{720 \, x^{3} - 720 \, x^{2} + 618 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 2648 \, x + 875}{32 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/32*(720*x^3 - 720*x^2 + 618*(4*x^2 - 4*x + 1)*log(2*x - 1) - 2648*x + 875)/(4
*x^2 - 4*x + 1)

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Sympy [A]  time = 0.262768, size = 29, normalized size = 0.76 \[ - \frac{45 x}{8} + \frac{2828 x - 875}{128 x^{2} - 128 x + 32} - \frac{309 \log{\left (2 x - 1 \right )}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-45*x/8 + (2828*x - 875)/(128*x**2 - 128*x + 32) - 309*log(2*x - 1)/16

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GIAC/XCAS [A]  time = 0.21656, size = 36, normalized size = 0.95 \[ -\frac{45}{8} \, x + \frac{7 \,{\left (404 \, x - 125\right )}}{32 \,{\left (2 \, x - 1\right )}^{2}} - \frac{309}{16} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-45/8*x + 7/32*(404*x - 125)/(2*x - 1)^2 - 309/16*ln(abs(2*x - 1))