Optimal. Leaf size=30 \[ -\frac{25 x^3}{2}-\frac{355 x^2}{8}-\frac{703 x}{8}-\frac{847}{16} \log (1-2 x) \]
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Rubi [A] time = 0.0104914, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{25 x^3}{2}-\frac{355 x^2}{8}-\frac{703 x}{8}-\frac{847}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac{703}{8}-\frac{355 x}{4}-\frac{75 x^2}{2}-\frac{847}{8 (-1+2 x)}\right ) \, dx\\ &=-\frac{703 x}{8}-\frac{355 x^2}{8}-\frac{25 x^3}{2}-\frac{847}{16} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0095034, size = 27, normalized size = 0.9 \[ \frac{1}{32} \left (-400 x^3-1420 x^2-2812 x-1694 \log (1-2 x)+1811\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 23, normalized size = 0.8 \begin{align*} -{\frac{25\,{x}^{3}}{2}}-{\frac{355\,{x}^{2}}{8}}-{\frac{703\,x}{8}}-{\frac{847\,\ln \left ( 2\,x-1 \right ) }{16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08572, size = 30, normalized size = 1. \begin{align*} -\frac{25}{2} \, x^{3} - \frac{355}{8} \, x^{2} - \frac{703}{8} \, x - \frac{847}{16} \, \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 = 1.41817, size = 74, normalized size = 2.47 \begin{align*} -\frac{25}{2} \, x^{3} - \frac{355}{8} \, x^{2} - \frac{703}{8} \, x - \frac{847}{16} \, \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 = 0.087968, size = 29, normalized size = 0.97 \begin{align*} - \frac{25 x^{3}}{2} - \frac{355 x^{2}}{8} - \frac{703 x}{8} - \frac{847 \log{\left (2 x - 1 \right )}}{16} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.24392, size = 31, normalized size = 1.03 \begin{align*} -\frac{25}{2} \, x^{3} - \frac{355}{8} \, x^{2} - \frac{703}{8} \, x - \frac{847}{16} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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