Optimal. Leaf size=45 \[ \frac{50 x^2}{27}-\frac{20 x}{3}+\frac{518}{243 (3 x+2)}-\frac{49}{486 (3 x+2)^2}+\frac{503}{81} \log (3 x+2) \]
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Rubi [A] time = 0.0212613, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{50 x^2}{27}-\frac{20 x}{3}+\frac{518}{243 (3 x+2)}-\frac{49}{486 (3 x+2)^2}+\frac{503}{81} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^3} \, dx &=\int \left (-\frac{20}{3}+\frac{100 x}{27}+\frac{49}{81 (2+3 x)^3}-\frac{518}{81 (2+3 x)^2}+\frac{503}{27 (2+3 x)}\right ) \, dx\\ &=-\frac{20 x}{3}+\frac{50 x^2}{27}-\frac{49}{486 (2+3 x)^2}+\frac{518}{243 (2+3 x)}+\frac{503}{81} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0167365, size = 42, normalized size = 0.93 \[ \frac{503}{81} \log (3 x+2)-\frac{-900 x^4+2040 x^3+6480 x^2+4508 x+913}{54 (3 x+2)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{20\,x}{3}}+{\frac{50\,{x}^{2}}{27}}-{\frac{49}{486\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{518}{486+729\,x}}+{\frac{503\,\ln \left ( 2+3\,x \right ) }{81}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.45356, size = 49, normalized size = 1.09 \begin{align*} \frac{50}{27} \, x^{2} - \frac{20}{3} \, x + \frac{7 \,{\left (444 \, x + 289\right )}}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{503}{81} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47322, size = 157, normalized size = 3.49 \begin{align*} \frac{8100 \, x^{4} - 18360 \, x^{3} - 35280 \, x^{2} + 3018 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 9852 \, x + 2023}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.115924, size = 36, normalized size = 0.8 \begin{align*} \frac{50 x^{2}}{27} - \frac{20 x}{3} + \frac{3108 x + 2023}{4374 x^{2} + 5832 x + 1944} + \frac{503 \log{\left (3 x + 2 \right )}}{81} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.83239, size = 43, normalized size = 0.96 \begin{align*} \frac{50}{27} \, x^{2} - \frac{20}{3} \, x + \frac{7 \,{\left (444 \, x + 289\right )}}{486 \,{\left (3 \, x + 2\right )}^{2}} + \frac{503}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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