Optimal. Leaf size=23 \[ -\frac{3 x^2}{5}+\frac{13 x}{25}+\frac{11}{125} \log (5 x+3) \]
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Rubi [A] time = 0.0091311, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{3 x^2}{5}+\frac{13 x}{25}+\frac{11}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)}{3+5 x} \, dx &=\int \left (\frac{13}{25}-\frac{6 x}{5}+\frac{11}{25 (3+5 x)}\right ) \, dx\\ &=\frac{13 x}{25}-\frac{3 x^2}{5}+\frac{11}{125} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0046593, size = 22, normalized size = 0.96 \[ \frac{1}{125} \left (-75 x^2+65 x+11 \log (5 x+3)+66\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 18, normalized size = 0.8 \begin{align*}{\frac{13\,x}{25}}-{\frac{3\,{x}^{2}}{5}}+{\frac{11\,\ln \left ( 3+5\,x \right ) }{125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.35828, size = 23, normalized size = 1. \begin{align*} -\frac{3}{5} \, x^{2} + \frac{13}{25} \, x + \frac{11}{125} \, \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 = 1.53792, size = 57, normalized size = 2.48 \begin{align*} -\frac{3}{5} \, x^{2} + \frac{13}{25} \, x + \frac{11}{125} \, \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 = 0.07776, size = 20, normalized size = 0.87 \begin{align*} - \frac{3 x^{2}}{5} + \frac{13 x}{25} + \frac{11 \log{\left (5 x + 3 \right )}}{125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.76672, size = 24, normalized size = 1.04 \begin{align*} -\frac{3}{5} \, x^{2} + \frac{13}{25} \, x + \frac{11}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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