Optimal. Leaf size=48 \[ \frac{125 x^4}{9}-\frac{800 x^3}{81}-\frac{305 x^2}{54}+\frac{1271 x}{243}+\frac{49}{729 (3 x+2)}+\frac{763}{729} \log (3 x+2) \]
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Rubi [A] time = 0.0230949, antiderivative size = 48, 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} \[ \frac{125 x^4}{9}-\frac{800 x^3}{81}-\frac{305 x^2}{54}+\frac{1271 x}{243}+\frac{49}{729 (3 x+2)}+\frac{763}{729} \log (3 x+2) \]
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)^2} \, dx &=\int \left (\frac{1271}{243}-\frac{305 x}{27}-\frac{800 x^2}{27}+\frac{500 x^3}{9}-\frac{49}{243 (2+3 x)^2}+\frac{763}{243 (2+3 x)}\right ) \, dx\\ &=\frac{1271 x}{243}-\frac{305 x^2}{54}-\frac{800 x^3}{81}+\frac{125 x^4}{9}+\frac{49}{729 (2+3 x)}+\frac{763}{729} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0285264, size = 49, normalized size = 1.02 \[ \frac{182250 x^5-8100 x^4-160515 x^3+19224 x^2+50052 x+4578 (3 x+2) \log (30 x+20)+3158}{4374 (3 x+2)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 37, normalized size = 0.8 \begin{align*}{\frac{1271\,x}{243}}-{\frac{305\,{x}^{2}}{54}}-{\frac{800\,{x}^{3}}{81}}+{\frac{125\,{x}^{4}}{9}}+{\frac{49}{1458+2187\,x}}+{\frac{763\,\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 = 0.995059, size = 49, normalized size = 1.02 \begin{align*} \frac{125}{9} \, x^{4} - \frac{800}{81} \, x^{3} - \frac{305}{54} \, x^{2} + \frac{1271}{243} \, x + \frac{49}{729 \,{\left (3 \, x + 2\right )}} + \frac{763}{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 = 1.52547, size = 147, normalized size = 3.06 \begin{align*} \frac{60750 \, x^{5} - 2700 \, x^{4} - 53505 \, x^{3} + 6408 \, x^{2} + 1526 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 15252 \, x + 98}{1458 \,{\left (3 \, x + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.103381, size = 41, normalized size = 0.85 \begin{align*} \frac{125 x^{4}}{9} - \frac{800 x^{3}}{81} - \frac{305 x^{2}}{54} + \frac{1271 x}{243} + \frac{763 \log{\left (3 x + 2 \right )}}{729} + \frac{49}{2187 x + 1458} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.60323, size = 89, normalized size = 1.85 \begin{align*} -\frac{1}{4374} \,{\left (3 \, x + 2\right )}^{4}{\left (\frac{7600}{3 \, x + 2} - \frac{24855}{{\left (3 \, x + 2\right )}^{2}} + \frac{24594}{{\left (3 \, x + 2\right )}^{3}} - 750\right )} + \frac{49}{729 \,{\left (3 \, x + 2\right )}} - \frac{763}{729} \, \log \left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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