Optimal. Leaf size=30 \[ -\frac{6 x^3}{5}-\frac{21 x^2}{50}+\frac{163 x}{125}+\frac{11}{625} \log (5 x+3) \]
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Rubi [A] time = 0.0111338, 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} \[ -\frac{6 x^3}{5}-\frac{21 x^2}{50}+\frac{163 x}{125}+\frac{11}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)^2}{3+5 x} \, dx &=\int \left (\frac{163}{125}-\frac{21 x}{25}-\frac{18 x^2}{5}+\frac{11}{125 (3+5 x)}\right ) \, dx\\ &=\frac{163 x}{125}-\frac{21 x^2}{50}-\frac{6 x^3}{5}+\frac{11}{625} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0094619, size = 27, normalized size = 0.9 \[ \frac{-1500 x^3-525 x^2+1630 x+22 \log (5 x+3)+843}{1250} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 23, normalized size = 0.8 \begin{align*}{\frac{163\,x}{125}}-{\frac{21\,{x}^{2}}{50}}-{\frac{6\,{x}^{3}}{5}}+{\frac{11\,\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 = 1.03053, size = 30, normalized size = 1. \begin{align*} -\frac{6}{5} \, x^{3} - \frac{21}{50} \, x^{2} + \frac{163}{125} \, x + \frac{11}{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 = 1.49581, size = 76, normalized size = 2.53 \begin{align*} -\frac{6}{5} \, x^{3} - \frac{21}{50} \, x^{2} + \frac{163}{125} \, x + \frac{11}{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 = 0.083089, size = 27, normalized size = 0.9 \begin{align*} - \frac{6 x^{3}}{5} - \frac{21 x^{2}}{50} + \frac{163 x}{125} + \frac{11 \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 = 1.39227, size = 31, normalized size = 1.03 \begin{align*} -\frac{6}{5} \, x^{3} - \frac{21}{50} \, x^{2} + \frac{163}{125} \, x + \frac{11}{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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