3.1332 \(\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^3} \, dx\)

Optimal. Leaf size=45 \[ -\frac{20 x^2}{27}+\frac{116 x}{27}-\frac{2009}{243 (3 x+2)}+\frac{343}{486 (3 x+2)^2}-\frac{518}{81} \log (3 x+2) \]

[Out]

(116*x)/27 - (20*x^2)/27 + 343/(486*(2 + 3*x)^2) - 2009/(243*(2 + 3*x)) - (518*L
og[2 + 3*x])/81

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Rubi [A]  time = 0.054711, antiderivative size = 45, 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 \[ -\frac{20 x^2}{27}+\frac{116 x}{27}-\frac{2009}{243 (3 x+2)}+\frac{343}{486 (3 x+2)^2}-\frac{518}{81} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(116*x)/27 - (20*x^2)/27 + 343/(486*(2 + 3*x)^2) - 2009/(243*(2 + 3*x)) - (518*L
og[2 + 3*x])/81

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{518 \log{\left (3 x + 2 \right )}}{81} + \int \frac{116}{27}\, dx - \frac{40 \int x\, dx}{27} - \frac{2009}{243 \left (3 x + 2\right )} + \frac{343}{486 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-518*log(3*x + 2)/81 + Integral(116/27, x) - 40*Integral(x, x)/27 - 2009/(243*(3
*x + 2)) + 343/(486*(3*x + 2)**2)

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Mathematica [A]  time = 0.0304589, size = 46, normalized size = 1.02 \[ -\frac{3240 x^4-14472 x^3-15030 x^2+15150 x+3108 (3 x+2)^2 \log (6 x+4)+11509}{486 (3 x+2)^2} \]

Antiderivative was successfully verified.

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

[Out]

-(11509 + 15150*x - 15030*x^2 - 14472*x^3 + 3240*x^4 + 3108*(2 + 3*x)^2*Log[4 +
6*x])/(486*(2 + 3*x)^2)

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Maple [A]  time = 0.01, size = 36, normalized size = 0.8 \[{\frac{116\,x}{27}}-{\frac{20\,{x}^{2}}{27}}+{\frac{343}{486\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{2009}{486+729\,x}}-{\frac{518\,\ln \left ( 2+3\,x \right ) }{81}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

116/27*x-20/27*x^2+343/486/(2+3*x)^2-2009/243/(2+3*x)-518/81*ln(2+3*x)

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Maxima [A]  time = 1.34837, size = 49, normalized size = 1.09 \[ -\frac{20}{27} \, x^{2} + \frac{116}{27} \, x - \frac{49 \,{\left (246 \, x + 157\right )}}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{518}{81} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20/27*x^2 + 116/27*x - 49/486*(246*x + 157)/(9*x^2 + 12*x + 4) - 518/81*log(3*x
+ 2)

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Fricas [A]  time = 0.216058, size = 70, normalized size = 1.56 \[ -\frac{3240 \, x^{4} - 14472 \, x^{3} - 23616 \, x^{2} + 3108 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 3702 \, x + 7693}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/486*(3240*x^4 - 14472*x^3 - 23616*x^2 + 3108*(9*x^2 + 12*x + 4)*log(3*x + 2)
+ 3702*x + 7693)/(9*x^2 + 12*x + 4)

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Sympy [A]  time = 0.269699, size = 36, normalized size = 0.8 \[ - \frac{20 x^{2}}{27} + \frac{116 x}{27} - \frac{12054 x + 7693}{4374 x^{2} + 5832 x + 1944} - \frac{518 \log{\left (3 x + 2 \right )}}{81} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20*x**2/27 + 116*x/27 - (12054*x + 7693)/(4374*x**2 + 5832*x + 1944) - 518*log(
3*x + 2)/81

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GIAC/XCAS [A]  time = 0.209486, size = 43, normalized size = 0.96 \[ -\frac{20}{27} \, x^{2} + \frac{116}{27} \, x - \frac{49 \,{\left (246 \, x + 157\right )}}{486 \,{\left (3 \, x + 2\right )}^{2}} - \frac{518}{81} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-20/27*x^2 + 116/27*x - 49/486*(246*x + 157)/(3*x + 2)^2 - 518/81*ln(abs(3*x + 2
))