Optimal. Leaf size=30 \[ \frac{20 x^3}{9}-\frac{32 x^2}{9}+\frac{65 x}{27}-\frac{49}{81} \log (3 x+2) \]
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Rubi [A] time = 0.0114052, antiderivative size = 30, 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} \[ \frac{20 x^3}{9}-\frac{32 x^2}{9}+\frac{65 x}{27}-\frac{49}{81} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)}{2+3 x} \, dx &=\int \left (\frac{65}{27}-\frac{64 x}{9}+\frac{20 x^2}{3}-\frac{49}{27 (2+3 x)}\right ) \, dx\\ &=\frac{65 x}{27}-\frac{32 x^2}{9}+\frac{20 x^3}{9}-\frac{49}{81} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0101094, size = 27, normalized size = 0.9 \[ \frac{1}{243} \left (540 x^3-864 x^2+585 x-147 \log (3 x+2)+934\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 23, normalized size = 0.8 \begin{align*}{\frac{65\,x}{27}}-{\frac{32\,{x}^{2}}{9}}+{\frac{20\,{x}^{3}}{9}}-{\frac{49\,\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 = 1.02672, size = 30, normalized size = 1. \begin{align*} \frac{20}{9} \, x^{3} - \frac{32}{9} \, x^{2} + \frac{65}{27} \, x - \frac{49}{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 = 1.45707, size = 70, normalized size = 2.33 \begin{align*} \frac{20}{9} \, x^{3} - \frac{32}{9} \, x^{2} + \frac{65}{27} \, x - \frac{49}{81} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.084244, size = 27, normalized size = 0.9 \begin{align*} \frac{20 x^{3}}{9} - \frac{32 x^{2}}{9} + \frac{65 x}{27} - \frac{49 \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 = 1.93782, size = 31, normalized size = 1.03 \begin{align*} \frac{20}{9} \, x^{3} - \frac{32}{9} \, x^{2} + \frac{65}{27} \, x - \frac{49}{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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