Optimal. Leaf size=44 \[ -\frac{81 x^5}{2}-\frac{3051 x^4}{16}-\frac{3321 x^3}{8}-\frac{18987 x^2}{32}-\frac{24875 x}{32}-\frac{26411}{64} \log (1-2 x) \]
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Rubi [A] time = 0.0161629, antiderivative size = 44, 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} \[ -\frac{81 x^5}{2}-\frac{3051 x^4}{16}-\frac{3321 x^3}{8}-\frac{18987 x^2}{32}-\frac{24875 x}{32}-\frac{26411}{64} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^4 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac{24875}{32}-\frac{18987 x}{16}-\frac{9963 x^2}{8}-\frac{3051 x^3}{4}-\frac{405 x^4}{2}-\frac{26411}{32 (-1+2 x)}\right ) \, dx\\ &=-\frac{24875 x}{32}-\frac{18987 x^2}{32}-\frac{3321 x^3}{8}-\frac{3051 x^4}{16}-\frac{81 x^5}{2}-\frac{26411}{64} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0130676, size = 37, normalized size = 0.84 \[ \frac{1}{256} \left (-10368 x^5-48816 x^4-106272 x^3-151896 x^2-199000 x-105644 \log (1-2 x)+154133\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 33, normalized size = 0.8 \begin{align*} -{\frac{81\,{x}^{5}}{2}}-{\frac{3051\,{x}^{4}}{16}}-{\frac{3321\,{x}^{3}}{8}}-{\frac{18987\,{x}^{2}}{32}}-{\frac{24875\,x}{32}}-{\frac{26411\,\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 = 1.01984, size = 43, normalized size = 0.98 \begin{align*} -\frac{81}{2} \, x^{5} - \frac{3051}{16} \, x^{4} - \frac{3321}{8} \, x^{3} - \frac{18987}{32} \, x^{2} - \frac{24875}{32} \, x - \frac{26411}{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 = 1.2521, size = 122, normalized size = 2.77 \begin{align*} -\frac{81}{2} \, x^{5} - \frac{3051}{16} \, x^{4} - \frac{3321}{8} \, x^{3} - \frac{18987}{32} \, x^{2} - \frac{24875}{32} \, x - \frac{26411}{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 = 0.091835, size = 42, normalized size = 0.95 \begin{align*} - \frac{81 x^{5}}{2} - \frac{3051 x^{4}}{16} - \frac{3321 x^{3}}{8} - \frac{18987 x^{2}}{32} - \frac{24875 x}{32} - \frac{26411 \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 = 2.41027, size = 45, normalized size = 1.02 \begin{align*} -\frac{81}{2} \, x^{5} - \frac{3051}{16} \, x^{4} - \frac{3321}{8} \, x^{3} - \frac{18987}{32} \, x^{2} - \frac{24875}{32} \, x - \frac{26411}{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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