Optimal. Leaf size=44 \[ -\frac{225 x^5}{2}-\frac{8175 x^4}{16}-\frac{25835 x^3}{24}-\frac{47939 x^2}{32}-\frac{61763 x}{32}-\frac{65219}{64} \log (1-2 x) \]
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Rubi [A] time = 0.0194679, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ -\frac{225 x^5}{2}-\frac{8175 x^4}{16}-\frac{25835 x^3}{24}-\frac{47939 x^2}{32}-\frac{61763 x}{32}-\frac{65219}{64} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)^3}{1-2 x} \, dx &=\int \left (-\frac{61763}{32}-\frac{47939 x}{16}-\frac{25835 x^2}{8}-\frac{8175 x^3}{4}-\frac{1125 x^4}{2}-\frac{65219}{32 (-1+2 x)}\right ) \, dx\\ &=-\frac{61763 x}{32}-\frac{47939 x^2}{32}-\frac{25835 x^3}{24}-\frac{8175 x^4}{16}-\frac{225 x^5}{2}-\frac{65219}{64} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0114682, size = 37, normalized size = 0.84 \[ \frac{1}{768} \left (-86400 x^5-392400 x^4-826720 x^3-1150536 x^2-1482312 x-782628 \log (1-2 x)+1159355\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 33, normalized size = 0.8 \begin{align*} -{\frac{225\,{x}^{5}}{2}}-{\frac{8175\,{x}^{4}}{16}}-{\frac{25835\,{x}^{3}}{24}}-{\frac{47939\,{x}^{2}}{32}}-{\frac{61763\,x}{32}}-{\frac{65219\,\ln \left ( 2\,x-1 \right ) }{64}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02213, size = 43, normalized size = 0.98 \begin{align*} -\frac{225}{2} \, x^{5} - \frac{8175}{16} \, x^{4} - \frac{25835}{24} \, x^{3} - \frac{47939}{32} \, x^{2} - \frac{61763}{32} \, x - \frac{65219}{64} \, \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 = 1.26818, size = 126, normalized size = 2.86 \begin{align*} -\frac{225}{2} \, x^{5} - \frac{8175}{16} \, x^{4} - \frac{25835}{24} \, x^{3} - \frac{47939}{32} \, x^{2} - \frac{61763}{32} \, x - \frac{65219}{64} \, \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 = 0.091516, size = 42, normalized size = 0.95 \begin{align*} - \frac{225 x^{5}}{2} - \frac{8175 x^{4}}{16} - \frac{25835 x^{3}}{24} - \frac{47939 x^{2}}{32} - \frac{61763 x}{32} - \frac{65219 \log{\left (2 x - 1 \right )}}{64} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.35696, size = 45, normalized size = 1.02 \begin{align*} -\frac{225}{2} \, x^{5} - \frac{8175}{16} \, x^{4} - \frac{25835}{24} \, x^{3} - \frac{47939}{32} \, x^{2} - \frac{61763}{32} \, x - \frac{65219}{64} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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