Optimal. Leaf size=27 \[ \frac{25 x}{4}+\frac{121}{8 (1-2 x)}+\frac{55}{4} \log (1-2 x) \]
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Rubi [A] time = 0.0112766, 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} \[ \frac{25 x}{4}+\frac{121}{8 (1-2 x)}+\frac{55}{4} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac{25}{4}+\frac{121}{4 (-1+2 x)^2}+\frac{55}{2 (-1+2 x)}\right ) \, dx\\ &=\frac{121}{8 (1-2 x)}+\frac{25 x}{4}+\frac{55}{4} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0110537, size = 26, normalized size = 0.96 \[ \frac{1}{8} \left (50 x+\frac{121}{1-2 x}+110 \log (1-2 x)-25\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 22, normalized size = 0.8 \begin{align*}{\frac{25\,x}{4}}+{\frac{55\,\ln \left ( 2\,x-1 \right ) }{4}}-{\frac{121}{16\,x-8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.29747, size = 28, normalized size = 1.04 \begin{align*} \frac{25}{4} \, x - \frac{121}{8 \,{\left (2 \, x - 1\right )}} + \frac{55}{4} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.23393, size = 90, normalized size = 3.33 \begin{align*} \frac{100 \, x^{2} + 110 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 50 \, x - 121}{8 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.090339, size = 20, normalized size = 0.74 \begin{align*} \frac{25 x}{4} + \frac{55 \log{\left (2 x - 1 \right )}}{4} - \frac{121}{16 x - 8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.03121, size = 43, normalized size = 1.59 \begin{align*} \frac{25}{4} \, x - \frac{121}{8 \,{\left (2 \, x - 1\right )}} - \frac{55}{4} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) - \frac{25}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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