3.1169 \(\int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^3} \, dx\)

Optimal. Leaf size=45 \[ -\frac{125 x^2}{27}+\frac{175 x}{27}-\frac{107}{243 (3 x+2)}+\frac{7}{486 (3 x+2)^2}-\frac{185}{81} \log (3 x+2) \]

[Out]

(175*x)/27 - (125*x^2)/27 + 7/(486*(2 + 3*x)^2) - 107/(243*(2 + 3*x)) - (185*Log
[2 + 3*x])/81

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Rubi [A]  time = 0.0573576, 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 \[ -\frac{125 x^2}{27}+\frac{175 x}{27}-\frac{107}{243 (3 x+2)}+\frac{7}{486 (3 x+2)^2}-\frac{185}{81} \log (3 x+2) \]

Antiderivative was successfully verified.

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

[Out]

(175*x)/27 - (125*x^2)/27 + 7/(486*(2 + 3*x)^2) - 107/(243*(2 + 3*x)) - (185*Log
[2 + 3*x])/81

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ - \frac{185 \log{\left (3 x + 2 \right )}}{81} + \int \frac{175}{27}\, dx - \frac{250 \int x\, dx}{27} - \frac{107}{243 \left (3 x + 2\right )} + \frac{7}{486 \left (3 x + 2\right )^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-185*log(3*x + 2)/81 + Integral(175/27, x) - 250*Integral(x, x)/27 - 107/(243*(3
*x + 2)) + 7/(486*(3*x + 2)**2)

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Mathematica [A]  time = 0.0195324, size = 46, normalized size = 1.02 \[ \frac{-6750 x^4+450 x^3+18900 x^2+16386 x-370 (3 x+2)^2 \log (3 x+2)+3993}{162 (3 x+2)^2} \]

Antiderivative was successfully verified.

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

[Out]

(3993 + 16386*x + 18900*x^2 + 450*x^3 - 6750*x^4 - 370*(2 + 3*x)^2*Log[2 + 3*x])
/(162*(2 + 3*x)^2)

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Maple [A]  time = 0.01, size = 36, normalized size = 0.8 \[{\frac{175\,x}{27}}-{\frac{125\,{x}^{2}}{27}}+{\frac{7}{486\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{107}{486+729\,x}}-{\frac{185\,\ln \left ( 2+3\,x \right ) }{81}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

175/27*x-125/27*x^2+7/486/(2+3*x)^2-107/243/(2+3*x)-185/81*ln(2+3*x)

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Maxima [A]  time = 1.34401, size = 49, normalized size = 1.09 \[ -\frac{125}{27} \, x^{2} + \frac{175}{27} \, x - \frac{642 \, x + 421}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{185}{81} \, \log \left (3 \, x + 2\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/27*x^2 + 175/27*x - 1/486*(642*x + 421)/(9*x^2 + 12*x + 4) - 185/81*log(3*x
+ 2)

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Fricas [A]  time = 0.217323, size = 70, normalized size = 1.56 \[ -\frac{20250 \, x^{4} - 1350 \, x^{3} - 28800 \, x^{2} + 1110 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 11958 \, x + 421}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/486*(20250*x^4 - 1350*x^3 - 28800*x^2 + 1110*(9*x^2 + 12*x + 4)*log(3*x + 2)
- 11958*x + 421)/(9*x^2 + 12*x + 4)

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Sympy [A]  time = 0.273801, size = 36, normalized size = 0.8 \[ - \frac{125 x^{2}}{27} + \frac{175 x}{27} - \frac{642 x + 421}{4374 x^{2} + 5832 x + 1944} - \frac{185 \log{\left (3 x + 2 \right )}}{81} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*x**2/27 + 175*x/27 - (642*x + 421)/(4374*x**2 + 5832*x + 1944) - 185*log(3*
x + 2)/81

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GIAC/XCAS [A]  time = 0.21225, size = 43, normalized size = 0.96 \[ -\frac{125}{27} \, x^{2} + \frac{175}{27} \, x - \frac{642 \, x + 421}{486 \,{\left (3 \, x + 2\right )}^{2}} - \frac{185}{81} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/27*x^2 + 175/27*x - 1/486*(642*x + 421)/(3*x + 2)^2 - 185/81*ln(abs(3*x + 2
))