Optimal. Leaf size=41 \[ -\frac{40 x^3}{27}+\frac{134 x^2}{27}-\frac{286 x}{27}+\frac{343}{243 (3 x+2)}+\frac{2009}{243} \log (3 x+2) \]
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Rubi [A] time = 0.0188105, antiderivative size = 41, 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, Rules used = {77} \[ -\frac{40 x^3}{27}+\frac{134 x^2}{27}-\frac{286 x}{27}+\frac{343}{243 (3 x+2)}+\frac{2009}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^2} \, dx &=\int \left (-\frac{286}{27}+\frac{268 x}{27}-\frac{40 x^2}{9}-\frac{343}{81 (2+3 x)^2}+\frac{2009}{81 (2+3 x)}\right ) \, dx\\ &=-\frac{286 x}{27}+\frac{134 x^2}{27}-\frac{40 x^3}{27}+\frac{343}{243 (2+3 x)}+\frac{2009}{243} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0138822, size = 44, normalized size = 1.07 \[ \frac{-2160 x^4+5796 x^3-10620 x^2-4113 x+4018 (3 x+2) \log (6 x+4)+4808}{486 (3 x+2)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 32, normalized size = 0.8 \begin{align*} -{\frac{286\,x}{27}}+{\frac{134\,{x}^{2}}{27}}-{\frac{40\,{x}^{3}}{27}}+{\frac{343}{486+729\,x}}+{\frac{2009\,\ln \left ( 2+3\,x \right ) }{243}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01015, size = 42, normalized size = 1.02 \begin{align*} -\frac{40}{27} \, x^{3} + \frac{134}{27} \, x^{2} - \frac{286}{27} \, x + \frac{343}{243 \,{\left (3 \, x + 2\right )}} + \frac{2009}{243} \, \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 = 1.21906, size = 130, normalized size = 3.17 \begin{align*} -\frac{1080 \, x^{4} - 2898 \, x^{3} + 5310 \, x^{2} - 2009 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 5148 \, x - 343}{243 \,{\left (3 \, x + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.100062, size = 34, normalized size = 0.83 \begin{align*} - \frac{40 x^{3}}{27} + \frac{134 x^{2}}{27} - \frac{286 x}{27} + \frac{2009 \log{\left (3 x + 2 \right )}}{243} + \frac{343}{729 x + 486} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.93421, size = 77, normalized size = 1.88 \begin{align*} \frac{2}{729} \,{\left (3 \, x + 2\right )}^{3}{\left (\frac{321}{3 \, x + 2} - \frac{2331}{{\left (3 \, x + 2\right )}^{2}} - 20\right )} + \frac{343}{243 \,{\left (3 \, x + 2\right )}} - \frac{2009}{243} \, \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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