Optimal. Leaf size=27 \[ \frac{4 x}{25}-\frac{121}{125 (5 x+3)}-\frac{44}{125} \log (5 x+3) \]
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Rubi [A] time = 0.0096519, antiderivative size = 27, 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} \[ \frac{4 x}{25}-\frac{121}{125 (5 x+3)}-\frac{44}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(3+5 x)^2} \, dx &=\int \left (\frac{4}{25}+\frac{121}{25 (3+5 x)^2}-\frac{44}{25 (3+5 x)}\right ) \, dx\\ &=\frac{4 x}{25}-\frac{121}{125 (3+5 x)}-\frac{44}{125} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0103306, size = 34, normalized size = 1.26 \[ \frac{100 x^2+10 x-44 (5 x+3) \log (10 x+6)-151}{125 (5 x+3)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 22, normalized size = 0.8 \begin{align*}{\frac{4\,x}{25}}-{\frac{121}{375+625\,x}}-{\frac{44\,\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 = 1.11889, size = 28, normalized size = 1.04 \begin{align*} \frac{4}{25} \, x - \frac{121}{125 \,{\left (5 \, x + 3\right )}} - \frac{44}{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 = 1.55409, size = 92, normalized size = 3.41 \begin{align*} \frac{100 \, x^{2} - 44 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 60 \, x - 121}{125 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.091352, size = 20, normalized size = 0.74 \begin{align*} \frac{4 x}{25} - \frac{44 \log{\left (5 x + 3 \right )}}{125} - \frac{121}{625 x + 375} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.12781, size = 43, normalized size = 1.59 \begin{align*} \frac{4}{25} \, x - \frac{121}{125 \,{\left (5 \, x + 3\right )}} + \frac{44}{125} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{12}{125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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