Optimal. Leaf size=52 \[ \frac{500 x^3}{81}-\frac{100 x^2}{9}+\frac{895 x}{81}-\frac{763}{729 (3 x+2)}+\frac{49}{1458 (3 x+2)^2}-\frac{4099}{729} \log (3 x+2) \]
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Rubi [A] time = 0.0236817, antiderivative size = 52, 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} \[ \frac{500 x^3}{81}-\frac{100 x^2}{9}+\frac{895 x}{81}-\frac{763}{729 (3 x+2)}+\frac{49}{1458 (3 x+2)^2}-\frac{4099}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^3} \, dx &=\int \left (\frac{895}{81}-\frac{200 x}{9}+\frac{500 x^2}{27}-\frac{49}{243 (2+3 x)^3}+\frac{763}{243 (2+3 x)^2}-\frac{4099}{243 (2+3 x)}\right ) \, dx\\ &=\frac{895 x}{81}-\frac{100 x^2}{9}+\frac{500 x^3}{81}+\frac{49}{1458 (2+3 x)^2}-\frac{763}{729 (2+3 x)}-\frac{4099}{729} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0309842, size = 51, normalized size = 0.98 \[ \frac{243000 x^5-113400 x^4-40230 x^3+941940 x^2+921426 x-24594 (3 x+2)^2 \log (30 x+20)+238271}{4374 (3 x+2)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 41, normalized size = 0.8 \begin{align*}{\frac{895\,x}{81}}-{\frac{100\,{x}^{2}}{9}}+{\frac{500\,{x}^{3}}{81}}+{\frac{49}{1458\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{763}{1458+2187\,x}}-{\frac{4099\,\ln \left ( 2+3\,x \right ) }{729}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03509, size = 55, normalized size = 1.06 \begin{align*} \frac{500}{81} \, x^{3} - \frac{100}{9} \, x^{2} + \frac{895}{81} \, x - \frac{7 \,{\left (218 \, x + 143\right )}}{486 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{4099}{729} \, \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 = 1.43772, size = 178, normalized size = 3.42 \begin{align*} \frac{81000 \, x^{5} - 37800 \, x^{4} - 13410 \, x^{3} + 128520 \, x^{2} - 8198 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) + 59862 \, x - 3003}{1458 \,{\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 = 0.11924, size = 42, normalized size = 0.81 \begin{align*} \frac{500 x^{3}}{81} - \frac{100 x^{2}}{9} + \frac{895 x}{81} - \frac{1526 x + 1001}{4374 x^{2} + 5832 x + 1944} - \frac{4099 \log{\left (3 x + 2 \right )}}{729} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.62365, size = 50, normalized size = 0.96 \begin{align*} \frac{500}{81} \, x^{3} - \frac{100}{9} \, x^{2} + \frac{895}{81} \, x - \frac{7 \,{\left (218 \, x + 143\right )}}{486 \,{\left (3 \, x + 2\right )}^{2}} - \frac{4099}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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