Optimal. Leaf size=30 \[ \frac{4 x^3}{5}-\frac{28 x^2}{25}+\frac{43 x}{125}+\frac{121}{625} \log (5 x+3) \]
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Rubi [A] time = 0.0105243, 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} \[ \frac{4 x^3}{5}-\frac{28 x^2}{25}+\frac{43 x}{125}+\frac{121}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (2+3 x)}{3+5 x} \, dx &=\int \left (\frac{43}{125}-\frac{56 x}{25}+\frac{12 x^2}{5}+\frac{121}{125 (3+5 x)}\right ) \, dx\\ &=\frac{43 x}{125}-\frac{28 x^2}{25}+\frac{4 x^3}{5}+\frac{121}{625} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0096473, size = 27, normalized size = 0.9 \[ \frac{1}{625} \left (500 x^3-700 x^2+215 x+121 \log (5 x+3)+489\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 23, normalized size = 0.8 \begin{align*}{\frac{43\,x}{125}}-{\frac{28\,{x}^{2}}{25}}+{\frac{4\,{x}^{3}}{5}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00252, size = 30, normalized size = 1. \begin{align*} \frac{4}{5} \, x^{3} - \frac{28}{25} \, x^{2} + \frac{43}{125} \, x + \frac{121}{625} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47814, size = 74, normalized size = 2.47 \begin{align*} \frac{4}{5} \, x^{3} - \frac{28}{25} \, x^{2} + \frac{43}{125} \, x + \frac{121}{625} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.082155, size = 27, normalized size = 0.9 \begin{align*} \frac{4 x^{3}}{5} - \frac{28 x^{2}}{25} + \frac{43 x}{125} + \frac{121 \log{\left (5 x + 3 \right )}}{625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.67282, size = 31, normalized size = 1.03 \begin{align*} \frac{4}{5} \, x^{3} - \frac{28}{25} \, x^{2} + \frac{43}{125} \, x + \frac{121}{625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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