3.1333 \(\int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx\)

Optimal. Leaf size=49 \[ -\frac{40 x}{81}+\frac{518}{81 (3 x+2)}-\frac{2009}{486 (3 x+2)^2}+\frac{343}{729 (3 x+2)^3}+\frac{428}{243} \log (3 x+2) \]

[Out]

(-40*x)/81 + 343/(729*(2 + 3*x)^3) - 2009/(486*(2 + 3*x)^2) + 518/(81*(2 + 3*x))
+ (428*Log[2 + 3*x])/243

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Rubi [A]  time = 0.0541731, antiderivative size = 49, 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 \[ -\frac{40 x}{81}+\frac{518}{81 (3 x+2)}-\frac{2009}{486 (3 x+2)^2}+\frac{343}{729 (3 x+2)^3}+\frac{428}{243} \log (3 x+2) \]

Antiderivative was successfully verified.

[In]  Int[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^4,x]

[Out]

(-40*x)/81 + 343/(729*(2 + 3*x)^3) - 2009/(486*(2 + 3*x)^2) + 518/(81*(2 + 3*x))
+ (428*Log[2 + 3*x])/243

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{428 \log{\left (3 x + 2 \right )}}{243} + \int \left (- \frac{40}{81}\right )\, dx + \frac{518}{81 \left (3 x + 2\right )} - \frac{2009}{486 \left (3 x + 2\right )^{2}} + \frac{343}{729 \left (3 x + 2\right )^{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3*(3+5*x)/(2+3*x)**4,x)

[Out]

428*log(3*x + 2)/243 + Integral(-40/81, x) + 518/(81*(3*x + 2)) - 2009/(486*(3*x
+ 2)**2) + 343/(729*(3*x + 2)**3)

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Mathematica [A]  time = 0.0255186, size = 46, normalized size = 0.94 \[ \frac{-19440 x^4-51840 x^3+32076 x^2+70767 x+2568 (3 x+2)^3 \log (3 x+2)+22088}{1458 (3 x+2)^3} \]

Antiderivative was successfully verified.

[In]  Integrate[((1 - 2*x)^3*(3 + 5*x))/(2 + 3*x)^4,x]

[Out]

(22088 + 70767*x + 32076*x^2 - 51840*x^3 - 19440*x^4 + 2568*(2 + 3*x)^3*Log[2 +
3*x])/(1458*(2 + 3*x)^3)

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Maple [A]  time = 0.01, size = 40, normalized size = 0.8 \[ -{\frac{40\,x}{81}}+{\frac{343}{729\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{2009}{486\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{518}{162+243\,x}}+{\frac{428\,\ln \left ( 2+3\,x \right ) }{243}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(3+5*x)/(2+3*x)^4,x)

[Out]

-40/81*x+343/729/(2+3*x)^3-2009/486/(2+3*x)^2+518/81/(2+3*x)+428/243*ln(2+3*x)

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Maxima [A]  time = 1.34785, size = 55, normalized size = 1.12 \[ -\frac{40}{81} \, x + \frac{7 \,{\left (11988 \, x^{2} + 13401 \, x + 3704\right )}}{1458 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{428}{243} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^4,x, algorithm="maxima")

[Out]

-40/81*x + 7/1458*(11988*x^2 + 13401*x + 3704)/(27*x^3 + 54*x^2 + 36*x + 8) + 42
8/243*log(3*x + 2)

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Fricas [A]  time = 0.210349, size = 84, normalized size = 1.71 \[ -\frac{19440 \, x^{4} + 38880 \, x^{3} - 57996 \, x^{2} - 2568 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 88047 \, x - 25928}{1458 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^4,x, algorithm="fricas")

[Out]

-1/1458*(19440*x^4 + 38880*x^3 - 57996*x^2 - 2568*(27*x^3 + 54*x^2 + 36*x + 8)*l
og(3*x + 2) - 88047*x - 25928)/(27*x^3 + 54*x^2 + 36*x + 8)

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Sympy [A]  time = 0.320873, size = 39, normalized size = 0.8 \[ - \frac{40 x}{81} + \frac{83916 x^{2} + 93807 x + 25928}{39366 x^{3} + 78732 x^{2} + 52488 x + 11664} + \frac{428 \log{\left (3 x + 2 \right )}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(3+5*x)/(2+3*x)**4,x)

[Out]

-40*x/81 + (83916*x**2 + 93807*x + 25928)/(39366*x**3 + 78732*x**2 + 52488*x + 1
1664) + 428*log(3*x + 2)/243

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GIAC/XCAS [A]  time = 0.20569, size = 43, normalized size = 0.88 \[ -\frac{40}{81} \, x + \frac{7 \,{\left (11988 \, x^{2} + 13401 \, x + 3704\right )}}{1458 \,{\left (3 \, x + 2\right )}^{3}} + \frac{428}{243} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(2*x - 1)^3/(3*x + 2)^4,x, algorithm="giac")

[Out]

-40/81*x + 7/1458*(11988*x^2 + 13401*x + 3704)/(3*x + 2)^3 + 428/243*ln(abs(3*x
+ 2))