3.1331 \(\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^2} \, dx\)

Optimal. Leaf size=41 \[ -\frac{40 x^3}{27}+\frac{134 x^2}{27}-\frac{286 x}{27}+\frac{343}{243 (3 x+2)}+\frac{2009}{243} \log (3 x+2) \]

[Out]

(-286*x)/27 + (134*x^2)/27 - (40*x^3)/27 + 343/(243*(2 + 3*x)) + (2009*Log[2 + 3
*x])/243

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Rubi [A]  time = 0.0479219, antiderivative size = 41, 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 \[ -\frac{40 x^3}{27}+\frac{134 x^2}{27}-\frac{286 x}{27}+\frac{343}{243 (3 x+2)}+\frac{2009}{243} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(-286*x)/27 + (134*x^2)/27 - (40*x^3)/27 + 343/(243*(2 + 3*x)) + (2009*Log[2 + 3
*x])/243

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{40 x^{3}}{27} + \frac{2009 \log{\left (3 x + 2 \right )}}{243} + \int \left (- \frac{286}{27}\right )\, dx + \frac{268 \int x\, dx}{27} + \frac{343}{243 \left (3 x + 2\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-40*x**3/27 + 2009*log(3*x + 2)/243 + Integral(-286/27, x) + 268*Integral(x, x)/
27 + 343/(243*(3*x + 2))

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Mathematica [A]  time = 0.0202488, size = 44, normalized size = 1.07 \[ \frac{-2160 x^4+5796 x^3-10620 x^2-4113 x+4018 (3 x+2) \log (6 x+4)+4808}{486 (3 x+2)} \]

Antiderivative was successfully verified.

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

[Out]

(4808 - 4113*x - 10620*x^2 + 5796*x^3 - 2160*x^4 + 4018*(2 + 3*x)*Log[4 + 6*x])/
(486*(2 + 3*x))

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Maple [A]  time = 0.009, size = 32, normalized size = 0.8 \[ -{\frac{286\,x}{27}}+{\frac{134\,{x}^{2}}{27}}-{\frac{40\,{x}^{3}}{27}}+{\frac{343}{486+729\,x}}+{\frac{2009\,\ln \left ( 2+3\,x \right ) }{243}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-286/27*x+134/27*x^2-40/27*x^3+343/243/(2+3*x)+2009/243*ln(2+3*x)

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Maxima [A]  time = 1.34088, size = 42, normalized size = 1.02 \[ -\frac{40}{27} \, x^{3} + \frac{134}{27} \, x^{2} - \frac{286}{27} \, x + \frac{343}{243 \,{\left (3 \, x + 2\right )}} + \frac{2009}{243} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-40/27*x^3 + 134/27*x^2 - 286/27*x + 343/243/(3*x + 2) + 2009/243*log(3*x + 2)

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Fricas [A]  time = 0.212816, size = 57, normalized size = 1.39 \[ -\frac{1080 \, x^{4} - 2898 \, x^{3} + 5310 \, x^{2} - 2009 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 5148 \, x - 343}{243 \,{\left (3 \, x + 2\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/243*(1080*x^4 - 2898*x^3 + 5310*x^2 - 2009*(3*x + 2)*log(3*x + 2) + 5148*x -
343)/(3*x + 2)

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Sympy [A]  time = 0.213899, size = 34, normalized size = 0.83 \[ - \frac{40 x^{3}}{27} + \frac{134 x^{2}}{27} - \frac{286 x}{27} + \frac{2009 \log{\left (3 x + 2 \right )}}{243} + \frac{343}{729 x + 486} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-40*x**3/27 + 134*x**2/27 - 286*x/27 + 2009*log(3*x + 2)/243 + 343/(729*x + 486)

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GIAC/XCAS [A]  time = 0.206878, size = 77, normalized size = 1.88 \[ \frac{2}{729} \,{\left (3 \, x + 2\right )}^{3}{\left (\frac{321}{3 \, x + 2} - \frac{2331}{{\left (3 \, x + 2\right )}^{2}} - 20\right )} + \frac{343}{243 \,{\left (3 \, x + 2\right )}} - \frac{2009}{243} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/729*(3*x + 2)^3*(321/(3*x + 2) - 2331/(3*x + 2)^2 - 20) + 343/243/(3*x + 2) -
2009/243*ln(1/3*abs(3*x + 2)/(3*x + 2)^2)