Optimal. Leaf size=48 \[ \frac{675 x^4}{16}+\frac{945 x^3}{4}+\frac{21717 x^2}{32}+\frac{12973 x}{8}+\frac{41503}{64 (1-2 x)}+\frac{91091}{64} \log (1-2 x) \]
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Rubi [A] time = 0.0238557, antiderivative size = 48, 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} \[ \frac{675 x^4}{16}+\frac{945 x^3}{4}+\frac{21717 x^2}{32}+\frac{12973 x}{8}+\frac{41503}{64 (1-2 x)}+\frac{91091}{64} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^2} \, dx &=\int \left (\frac{12973}{8}+\frac{21717 x}{16}+\frac{2835 x^2}{4}+\frac{675 x^3}{4}+\frac{41503}{32 (-1+2 x)^2}+\frac{91091}{32 (-1+2 x)}\right ) \, dx\\ &=\frac{41503}{64 (1-2 x)}+\frac{12973 x}{8}+\frac{21717 x^2}{32}+\frac{945 x^3}{4}+\frac{675 x^4}{16}+\frac{91091}{64} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0144245, size = 49, normalized size = 1.02 \[ \frac{21600 x^5+110160 x^4+286992 x^3+656536 x^2-933610 x+364364 (2 x-1) \log (1-2 x)+93225}{256 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 37, normalized size = 0.8 \begin{align*}{\frac{675\,{x}^{4}}{16}}+{\frac{945\,{x}^{3}}{4}}+{\frac{21717\,{x}^{2}}{32}}+{\frac{12973\,x}{8}}+{\frac{91091\,\ln \left ( 2\,x-1 \right ) }{64}}-{\frac{41503}{128\,x-64}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.39468, size = 49, normalized size = 1.02 \begin{align*} \frac{675}{16} \, x^{4} + \frac{945}{4} \, x^{3} + \frac{21717}{32} \, x^{2} + \frac{12973}{8} \, x - \frac{41503}{64 \,{\left (2 \, x - 1\right )}} + \frac{91091}{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 = 1.18877, size = 154, normalized size = 3.21 \begin{align*} \frac{5400 \, x^{5} + 27540 \, x^{4} + 71748 \, x^{3} + 164134 \, x^{2} + 91091 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 103784 \, x - 41503}{64 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.104304, size = 41, normalized size = 0.85 \begin{align*} \frac{675 x^{4}}{16} + \frac{945 x^{3}}{4} + \frac{21717 x^{2}}{32} + \frac{12973 x}{8} + \frac{91091 \log{\left (2 x - 1 \right )}}{64} - \frac{41503}{128 x - 64} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.97705, size = 89, normalized size = 1.85 \begin{align*} \frac{1}{256} \,{\left (2 \, x - 1\right )}^{4}{\left (\frac{10260}{2 \, x - 1} + \frac{70164}{{\left (2 \, x - 1\right )}^{2}} + \frac{319816}{{\left (2 \, x - 1\right )}^{3}} + 675\right )} - \frac{41503}{64 \,{\left (2 \, x - 1\right )}} - \frac{91091}{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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