Optimal. Leaf size=30 \[ -\frac{15 x^3}{2}-\frac{219 x^2}{8}-\frac{443 x}{8}-\frac{539}{16} \log (1-2 x) \]
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Rubi [A] time = 0.0116269, 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} \[ -\frac{15 x^3}{2}-\frac{219 x^2}{8}-\frac{443 x}{8}-\frac{539}{16} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac{443}{8}-\frac{219 x}{4}-\frac{45 x^2}{2}-\frac{539}{8 (-1+2 x)}\right ) \, dx\\ &=-\frac{443 x}{8}-\frac{219 x^2}{8}-\frac{15 x^3}{2}-\frac{539}{16} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0095626, size = 27, normalized size = 0.9 \[ \frac{1}{32} \left (-240 x^3-876 x^2-1772 x-1078 \log (1-2 x)+1135\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 23, normalized size = 0.8 \begin{align*} -{\frac{15\,{x}^{3}}{2}}-{\frac{219\,{x}^{2}}{8}}-{\frac{443\,x}{8}}-{\frac{539\,\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 = 2.44637, size = 30, normalized size = 1. \begin{align*} -\frac{15}{2} \, x^{3} - \frac{219}{8} \, x^{2} - \frac{443}{8} \, x - \frac{539}{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 = 1.37939, size = 74, normalized size = 2.47 \begin{align*} -\frac{15}{2} \, x^{3} - \frac{219}{8} \, x^{2} - \frac{443}{8} \, x - \frac{539}{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 = 0.085979, size = 29, normalized size = 0.97 \begin{align*} - \frac{15 x^{3}}{2} - \frac{219 x^{2}}{8} - \frac{443 x}{8} - \frac{539 \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 = 2.28814, size = 31, normalized size = 1.03 \begin{align*} -\frac{15}{2} \, x^{3} - \frac{219}{8} \, x^{2} - \frac{443}{8} \, x - \frac{539}{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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