3.1562 \(\int \frac{(3+5 x)^3}{(1-2 x)^2} \, dx\)

Optimal. Leaf size=34 \[ \frac{125 x^2}{8}+\frac{175 x}{2}+\frac{1331}{16 (1-2 x)}+\frac{1815}{16} \log (1-2 x) \]

[Out]

1331/(16*(1 - 2*x)) + (175*x)/2 + (125*x^2)/8 + (1815*Log[1 - 2*x])/16

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Rubi [A]  time = 0.0329023, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{125 x^2}{8}+\frac{175 x}{2}+\frac{1331}{16 (1-2 x)}+\frac{1815}{16} \log (1-2 x) \]

Antiderivative was successfully verified.

[In]  Int[(3 + 5*x)^3/(1 - 2*x)^2,x]

[Out]

1331/(16*(1 - 2*x)) + (175*x)/2 + (125*x^2)/8 + (1815*Log[1 - 2*x])/16

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{1815 \log{\left (- 2 x + 1 \right )}}{16} + \int \frac{175}{2}\, dx + \frac{125 \int x\, dx}{4} + \frac{1331}{16 \left (- 2 x + 1\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1815*log(-2*x + 1)/16 + Integral(175/2, x) + 125*Integral(x, x)/4 + 1331/(16*(-2
*x + 1))

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Mathematica [A]  time = 0.0124976, size = 36, normalized size = 1.06 \[ \frac{1000 x^3+5100 x^2-5850 x+3630 (2 x-1) \log (1-2 x)-1137}{64 x-32} \]

Antiderivative was successfully verified.

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

[Out]

(-1137 - 5850*x + 5100*x^2 + 1000*x^3 + 3630*(-1 + 2*x)*Log[1 - 2*x])/(-32 + 64*
x)

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Maple [A]  time = 0.009, size = 27, normalized size = 0.8 \[{\frac{125\,{x}^{2}}{8}}+{\frac{175\,x}{2}}-{\frac{1331}{-16+32\,x}}+{\frac{1815\,\ln \left ( -1+2\,x \right ) }{16}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((3+5*x)^3/(1-2*x)^2,x)

[Out]

125/8*x^2+175/2*x-1331/16/(-1+2*x)+1815/16*ln(-1+2*x)

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Maxima [A]  time = 1.34372, size = 35, normalized size = 1.03 \[ \frac{125}{8} \, x^{2} + \frac{175}{2} \, x - \frac{1331}{16 \,{\left (2 \, x - 1\right )}} + \frac{1815}{16} \, \log \left (2 \, x - 1\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125/8*x^2 + 175/2*x - 1331/16/(2*x - 1) + 1815/16*log(2*x - 1)

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Fricas [A]  time = 0.214283, size = 50, normalized size = 1.47 \[ \frac{500 \, x^{3} + 2550 \, x^{2} + 1815 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 1400 \, x - 1331}{16 \,{\left (2 \, x - 1\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/16*(500*x^3 + 2550*x^2 + 1815*(2*x - 1)*log(2*x - 1) - 1400*x - 1331)/(2*x - 1
)

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Sympy [A]  time = 0.183773, size = 27, normalized size = 0.79 \[ \frac{125 x^{2}}{8} + \frac{175 x}{2} + \frac{1815 \log{\left (2 x - 1 \right )}}{16} - \frac{1331}{32 x - 16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

125*x**2/8 + 175*x/2 + 1815*log(2*x - 1)/16 - 1331/(32*x - 16)

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GIAC/XCAS [A]  time = 0.207559, size = 65, normalized size = 1.91 \[ \frac{25}{32} \,{\left (2 \, x - 1\right )}^{2}{\left (\frac{66}{2 \, x - 1} + 5\right )} - \frac{1331}{16 \,{\left (2 \, x - 1\right )}} - \frac{1815}{16} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

25/32*(2*x - 1)^2*(66/(2*x - 1) + 5) - 1331/16/(2*x - 1) - 1815/16*ln(1/2*abs(2*
x - 1)/(2*x - 1)^2)