Optimal. Leaf size=55 \[ \frac{405 x^5}{4}+\frac{9855 x^4}{16}+\frac{29277 x^3}{16}+\frac{15159 x^2}{4}+\frac{480841 x}{64}+\frac{290521}{128 (1-2 x)}+\frac{381073}{64} \log (1-2 x) \]
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Rubi [A] time = 0.0277852, antiderivative size = 55, 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} \[ \frac{405 x^5}{4}+\frac{9855 x^4}{16}+\frac{29277 x^3}{16}+\frac{15159 x^2}{4}+\frac{480841 x}{64}+\frac{290521}{128 (1-2 x)}+\frac{381073}{64} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac{480841}{64}+\frac{15159 x}{2}+\frac{87831 x^2}{16}+\frac{9855 x^3}{4}+\frac{2025 x^4}{4}+\frac{290521}{64 (-1+2 x)^2}+\frac{381073}{32 (-1+2 x)}\right ) \, dx\\ &=\frac{290521}{128 (1-2 x)}+\frac{480841 x}{64}+\frac{15159 x^2}{4}+\frac{29277 x^3}{16}+\frac{9855 x^4}{16}+\frac{405 x^5}{4}+\frac{381073}{64} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0189184, size = 54, normalized size = 0.98 \[ \frac{51840 x^6+289440 x^5+779184 x^4+1471920 x^3+2876552 x^2-4470254 x+1524292 (2 x-1) \log (1-2 x)+692403}{256 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 42, normalized size = 0.8 \begin{align*}{\frac{405\,{x}^{5}}{4}}+{\frac{9855\,{x}^{4}}{16}}+{\frac{29277\,{x}^{3}}{16}}+{\frac{15159\,{x}^{2}}{4}}+{\frac{480841\,x}{64}}+{\frac{381073\,\ln \left ( 2\,x-1 \right ) }{64}}-{\frac{290521}{256\,x-128}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03124, size = 55, normalized size = 1. \begin{align*} \frac{405}{4} \, x^{5} + \frac{9855}{16} \, x^{4} + \frac{29277}{16} \, x^{3} + \frac{15159}{4} \, x^{2} + \frac{480841}{64} \, x - \frac{290521}{128 \,{\left (2 \, x - 1\right )}} + \frac{381073}{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 = 1.32116, size = 181, normalized size = 3.29 \begin{align*} \frac{25920 \, x^{6} + 144720 \, x^{5} + 389592 \, x^{4} + 735960 \, x^{3} + 1438276 \, x^{2} + 762146 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 961682 \, x - 290521}{128 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.106513, size = 48, normalized size = 0.87 \begin{align*} \frac{405 x^{5}}{4} + \frac{9855 x^{4}}{16} + \frac{29277 x^{3}}{16} + \frac{15159 x^{2}}{4} + \frac{480841 x}{64} + \frac{381073 \log{\left (2 x - 1 \right )}}{64} - \frac{290521}{256 x - 128} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.02586, size = 101, normalized size = 1.84 \begin{align*} \frac{1}{256} \,{\left (2 \, x - 1\right )}^{5}{\left (\frac{13905}{2 \, x - 1} + \frac{106074}{{\left (2 \, x - 1\right )}^{2}} + \frac{485436}{{\left (2 \, x - 1\right )}^{3}} + \frac{1665902}{{\left (2 \, x - 1\right )}^{4}} + 810\right )} - \frac{290521}{128 \,{\left (2 \, x - 1\right )}} - \frac{381073}{64} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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