Optimal. Leaf size=34 \[ -\frac{4 x^2}{25}+\frac{108 x}{125}-\frac{1331}{625 (5 x+3)}-\frac{726}{625} \log (5 x+3) \]
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Rubi [A] time = 0.01423, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {43} \[ -\frac{4 x^2}{25}+\frac{108 x}{125}-\frac{1331}{625 (5 x+3)}-\frac{726}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3}{(3+5 x)^2} \, dx &=\int \left (\frac{108}{125}-\frac{8 x}{25}+\frac{1331}{125 (3+5 x)^2}-\frac{726}{125 (3+5 x)}\right ) \, dx\\ &=\frac{108 x}{125}-\frac{4 x^2}{25}-\frac{1331}{625 (3+5 x)}-\frac{726}{625} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0104083, size = 39, normalized size = 1.15 \[ \frac{-500 x^3+2400 x^2+395 x-726 (5 x+3) \log (10 x+6)-2066}{625 (5 x+3)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 27, normalized size = 0.8 \begin{align*}{\frac{108\,x}{125}}-{\frac{4\,{x}^{2}}{25}}-{\frac{1331}{1875+3125\,x}}-{\frac{726\,\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 = 1.43875, size = 35, normalized size = 1.03 \begin{align*} -\frac{4}{25} \, x^{2} + \frac{108}{125} \, x - \frac{1331}{625 \,{\left (5 \, x + 3\right )}} - \frac{726}{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 = 1.33547, size = 113, normalized size = 3.32 \begin{align*} -\frac{500 \, x^{3} - 2400 \, x^{2} + 726 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1620 \, x + 1331}{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 = 0.095176, size = 27, normalized size = 0.79 \begin{align*} - \frac{4 x^{2}}{25} + \frac{108 x}{125} - \frac{726 \log{\left (5 x + 3 \right )}}{625} - \frac{1331}{3125 x + 1875} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.33065, size = 65, normalized size = 1.91 \begin{align*} \frac{4}{625} \,{\left (5 \, x + 3\right )}^{2}{\left (\frac{33}{5 \, x + 3} - 1\right )} - \frac{1331}{625 \,{\left (5 \, x + 3\right )}} + \frac{726}{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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