Optimal. Leaf size=23 \[ -\frac{25 x^2}{4}-\frac{85 x}{4}-\frac{121}{8} \log (1-2 x) \]
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Rubi [A] time = 0.0088048, antiderivative size = 23, 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} \[ -\frac{25 x^2}{4}-\frac{85 x}{4}-\frac{121}{8} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac{85}{4}-\frac{25 x}{2}-\frac{121}{4 (-1+2 x)}\right ) \, dx\\ &=-\frac{85 x}{4}-\frac{25 x^2}{4}-\frac{121}{8} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0059653, size = 25, normalized size = 1.09 \[ \frac{1}{16} \left (-5 \left (20 x^2+68 x-39\right )-242 \log (1-2 x)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 18, normalized size = 0.8 \begin{align*} -{\frac{25\,{x}^{2}}{4}}-{\frac{85\,x}{4}}-{\frac{121\,\ln \left ( 2\,x-1 \right ) }{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.988985, size = 23, normalized size = 1. \begin{align*} -\frac{25}{4} \, x^{2} - \frac{85}{4} \, x - \frac{121}{8} \, \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 = 1.28252, size = 55, normalized size = 2.39 \begin{align*} -\frac{25}{4} \, x^{2} - \frac{85}{4} \, x - \frac{121}{8} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.080987, size = 22, normalized size = 0.96 \begin{align*} - \frac{25 x^{2}}{4} - \frac{85 x}{4} - \frac{121 \log{\left (2 x - 1 \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26556, size = 24, normalized size = 1.04 \begin{align*} -\frac{25}{4} \, x^{2} - \frac{85}{4} \, x - \frac{121}{8} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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