Optimal. Leaf size=23 \[ -\frac{15 x^2}{4}-\frac{53 x}{4}-\frac{77}{8} \log (1-2 x) \]
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Rubi [A] time = 0.0087319, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{15 x^2}{4}-\frac{53 x}{4}-\frac{77}{8} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac{53}{4}-\frac{15 x}{2}-\frac{77}{4 (-1+2 x)}\right ) \, dx\\ &=-\frac{53 x}{4}-\frac{15 x^2}{4}-\frac{77}{8} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0045626, size = 22, normalized size = 0.96 \[ \frac{1}{16} \left (-60 x^2-212 x-154 \log (1-2 x)+121\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 18, normalized size = 0.8 \begin{align*} -{\frac{15\,{x}^{2}}{4}}-{\frac{53\,x}{4}}-{\frac{77\,\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 = 1.09141, size = 23, normalized size = 1. \begin{align*} -\frac{15}{4} \, x^{2} - \frac{53}{4} \, x - \frac{77}{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 = 1.31319, size = 54, normalized size = 2.35 \begin{align*} -\frac{15}{4} \, x^{2} - \frac{53}{4} \, x - \frac{77}{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 = 0.081297, size = 22, normalized size = 0.96 \begin{align*} - \frac{15 x^{2}}{4} - \frac{53 x}{4} - \frac{77 \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 = 2.63064, size = 24, normalized size = 1.04 \begin{align*} -\frac{15}{4} \, x^{2} - \frac{53}{4} \, x - \frac{77}{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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