3.1334 \(\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^5} \, dx\)

Optimal. Leaf size=55 \[ -\frac{428}{243 (3 x+2)}+\frac{259}{81 (3 x+2)^2}-\frac{2009}{729 (3 x+2)^3}+\frac{343}{972 (3 x+2)^4}-\frac{40}{243} \log (3 x+2) \]

[Out]

343/(972*(2 + 3*x)^4) - 2009/(729*(2 + 3*x)^3) + 259/(81*(2 + 3*x)^2) - 428/(243
*(2 + 3*x)) - (40*Log[2 + 3*x])/243

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Rubi [A]  time = 0.0531095, antiderivative size = 55, 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 \[ -\frac{428}{243 (3 x+2)}+\frac{259}{81 (3 x+2)^2}-\frac{2009}{729 (3 x+2)^3}+\frac{343}{972 (3 x+2)^4}-\frac{40}{243} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

343/(972*(2 + 3*x)^4) - 2009/(729*(2 + 3*x)^3) + 259/(81*(2 + 3*x)^2) - 428/(243
*(2 + 3*x)) - (40*Log[2 + 3*x])/243

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Rubi in Sympy [A]  time = 8.82551, size = 46, normalized size = 0.84 \[ - \frac{40 \log{\left (3 x + 2 \right )}}{243} - \frac{428}{243 \left (3 x + 2\right )} + \frac{259}{81 \left (3 x + 2\right )^{2}} - \frac{2009}{729 \left (3 x + 2\right )^{3}} + \frac{343}{972 \left (3 x + 2\right )^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-40*log(3*x + 2)/243 - 428/(243*(3*x + 2)) + 259/(81*(3*x + 2)**2) - 2009/(729*(
3*x + 2)**3) + 343/(972*(3*x + 2)**4)

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Mathematica [A]  time = 0.0256246, size = 41, normalized size = 0.75 \[ -\frac{138672 x^3+193428 x^2+97116 x+480 (3 x+2)^4 \log (6 x+4)+18835}{2916 (3 x+2)^4} \]

Antiderivative was successfully verified.

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

[Out]

-(18835 + 97116*x + 193428*x^2 + 138672*x^3 + 480*(2 + 3*x)^4*Log[4 + 6*x])/(291
6*(2 + 3*x)^4)

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Maple [A]  time = 0.01, size = 46, normalized size = 0.8 \[{\frac{343}{972\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{2009}{729\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{259}{81\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{428}{486+729\,x}}-{\frac{40\,\ln \left ( 2+3\,x \right ) }{243}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

343/972/(2+3*x)^4-2009/729/(2+3*x)^3+259/81/(2+3*x)^2-428/243/(2+3*x)-40/243*ln(
2+3*x)

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Maxima [A]  time = 1.34772, size = 65, normalized size = 1.18 \[ -\frac{138672 \, x^{3} + 193428 \, x^{2} + 97116 \, x + 18835}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac{40}{243} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2916*(138672*x^3 + 193428*x^2 + 97116*x + 18835)/(81*x^4 + 216*x^3 + 216*x^2
+ 96*x + 16) - 40/243*log(3*x + 2)

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Fricas [A]  time = 0.214389, size = 90, normalized size = 1.64 \[ -\frac{138672 \, x^{3} + 193428 \, x^{2} + 480 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 97116 \, x + 18835}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2916*(138672*x^3 + 193428*x^2 + 480*(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)*
log(3*x + 2) + 97116*x + 18835)/(81*x^4 + 216*x^3 + 216*x^2 + 96*x + 16)

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Sympy [A]  time = 0.373495, size = 46, normalized size = 0.84 \[ - \frac{138672 x^{3} + 193428 x^{2} + 97116 x + 18835}{236196 x^{4} + 629856 x^{3} + 629856 x^{2} + 279936 x + 46656} - \frac{40 \log{\left (3 x + 2 \right )}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(138672*x**3 + 193428*x**2 + 97116*x + 18835)/(236196*x**4 + 629856*x**3 + 6298
56*x**2 + 279936*x + 46656) - 40*log(3*x + 2)/243

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GIAC/XCAS [A]  time = 0.216805, size = 74, normalized size = 1.35 \[ -\frac{428}{243 \,{\left (3 \, x + 2\right )}} + \frac{259}{81 \,{\left (3 \, x + 2\right )}^{2}} - \frac{2009}{729 \,{\left (3 \, x + 2\right )}^{3}} + \frac{343}{972 \,{\left (3 \, x + 2\right )}^{4}} + \frac{40}{243} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-428/243/(3*x + 2) + 259/81/(3*x + 2)^2 - 2009/729/(3*x + 2)^3 + 343/972/(3*x +
2)^4 + 40/243*ln(1/3*abs(3*x + 2)/(3*x + 2)^2)