3.1377 \(\int \frac{(1-2 x)^3}{3+5 x} \, dx\)

Optimal. Leaf size=30 \[ -\frac{8 x^3}{15}+\frac{42 x^2}{25}-\frac{402 x}{125}+\frac{1331}{625} \log (5 x+3) \]

[Out]

(-402*x)/125 + (42*x^2)/25 - (8*x^3)/15 + (1331*Log[3 + 5*x])/625

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Rubi [A]  time = 0.0254921, antiderivative size = 30, 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 \[ -\frac{8 x^3}{15}+\frac{42 x^2}{25}-\frac{402 x}{125}+\frac{1331}{625} \log (5 x+3) \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3/(3 + 5*x),x]

[Out]

(-402*x)/125 + (42*x^2)/25 - (8*x^3)/15 + (1331*Log[3 + 5*x])/625

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{8 x^{3}}{15} + \frac{1331 \log{\left (5 x + 3 \right )}}{625} + \int \left (- \frac{402}{125}\right )\, dx + \frac{84 \int x\, dx}{25} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8*x**3/15 + 1331*log(5*x + 3)/625 + Integral(-402/125, x) + 84*Integral(x, x)/2
5

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Mathematica [A]  time = 0.0111754, size = 27, normalized size = 0.9 \[ \frac{-1000 x^3+3150 x^2-6030 x+3993 \log (5 x+3)-4968}{1875} \]

Antiderivative was successfully verified.

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

[Out]

(-4968 - 6030*x + 3150*x^2 - 1000*x^3 + 3993*Log[3 + 5*x])/1875

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Maple [A]  time = 0.005, size = 23, normalized size = 0.8 \[ -{\frac{402\,x}{125}}+{\frac{42\,{x}^{2}}{25}}-{\frac{8\,{x}^{3}}{15}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{625}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3/(3+5*x),x)

[Out]

-402/125*x+42/25*x^2-8/15*x^3+1331/625*ln(3+5*x)

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Maxima [A]  time = 1.33983, size = 30, normalized size = 1. \[ -\frac{8}{15} \, x^{3} + \frac{42}{25} \, x^{2} - \frac{402}{125} \, x + \frac{1331}{625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/15*x^3 + 42/25*x^2 - 402/125*x + 1331/625*log(5*x + 3)

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Fricas [A]  time = 0.206493, size = 30, normalized size = 1. \[ -\frac{8}{15} \, x^{3} + \frac{42}{25} \, x^{2} - \frac{402}{125} \, x + \frac{1331}{625} \, \log \left (5 \, x + 3\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/15*x^3 + 42/25*x^2 - 402/125*x + 1331/625*log(5*x + 3)

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Sympy [A]  time = 0.148593, size = 27, normalized size = 0.9 \[ - \frac{8 x^{3}}{15} + \frac{42 x^{2}}{25} - \frac{402 x}{125} + \frac{1331 \log{\left (5 x + 3 \right )}}{625} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3/(3+5*x),x)

[Out]

-8*x**3/15 + 42*x**2/25 - 402*x/125 + 1331*log(5*x + 3)/625

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GIAC/XCAS [A]  time = 0.213909, size = 31, normalized size = 1.03 \[ -\frac{8}{15} \, x^{3} + \frac{42}{25} \, x^{2} - \frac{402}{125} \, x + \frac{1331}{625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-8/15*x^3 + 42/25*x^2 - 402/125*x + 1331/625*ln(abs(5*x + 3))