Optimal. Leaf size=34 \[ \frac{6 x^2}{25}-\frac{92 x}{125}-\frac{121}{625 (5 x+3)}+\frac{319}{625} \log (5 x+3) \]
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Rubi [A] time = 0.0142219, antiderivative size = 34, 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} \[ \frac{6 x^2}{25}-\frac{92 x}{125}-\frac{121}{625 (5 x+3)}+\frac{319}{625} \log (5 x+3) \]
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)^2} \, dx &=\int \left (-\frac{92}{125}+\frac{12 x}{25}+\frac{121}{125 (3+5 x)^2}+\frac{319}{125 (3+5 x)}\right ) \, dx\\ &=-\frac{92 x}{125}+\frac{6 x^2}{25}-\frac{121}{625 (3+5 x)}+\frac{319}{625} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0125446, size = 39, normalized size = 1.15 \[ \frac{1500 x^3-3700 x^2-835 x+638 (5 x+3) \log (10 x+6)+913}{1250 (5 x+3)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 27, normalized size = 0.8 \begin{align*} -{\frac{92\,x}{125}}+{\frac{6\,{x}^{2}}{25}}-{\frac{121}{1875+3125\,x}}+{\frac{319\,\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 = 2.67715, size = 35, normalized size = 1.03 \begin{align*} \frac{6}{25} \, x^{2} - \frac{92}{125} \, x - \frac{121}{625 \,{\left (5 \, x + 3\right )}} + \frac{319}{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 = 1.45722, size = 111, normalized size = 3.26 \begin{align*} \frac{750 \, x^{3} - 1850 \, x^{2} + 319 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1380 \, x - 121}{625 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.09666, size = 27, normalized size = 0.79 \begin{align*} \frac{6 x^{2}}{25} - \frac{92 x}{125} + \frac{319 \log{\left (5 x + 3 \right )}}{625} - \frac{121}{3125 x + 1875} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.6426, size = 65, normalized size = 1.91 \begin{align*} -\frac{2}{625} \,{\left (5 \, x + 3\right )}^{2}{\left (\frac{64}{5 \, x + 3} - 3\right )} - \frac{121}{625 \,{\left (5 \, x + 3\right )}} - \frac{319}{625} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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