Optimal. Leaf size=52 \[ -\frac {375 x^3}{8}-\frac {10425 x^2}{32}-\frac {5695 x}{4}-\frac {144837}{64 (1-2 x)}+\frac {65219}{128 (1-2 x)^2}-\frac {64317}{32} \log (1-2 x) \]
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Rubi [A] time = 0.03, antiderivative size = 52, normalized size of antiderivative = 1.00, 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} \[ -\frac {375 x^3}{8}-\frac {10425 x^2}{32}-\frac {5695 x}{4}-\frac {144837}{64 (1-2 x)}+\frac {65219}{128 (1-2 x)^2}-\frac {64317}{32} \log (1-2 x) \]
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)^3} \, dx &=\int \left (-\frac {5695}{4}-\frac {10425 x}{16}-\frac {1125 x^2}{8}-\frac {65219}{32 (-1+2 x)^3}-\frac {144837}{32 (-1+2 x)^2}-\frac {64317}{16 (-1+2 x)}\right ) \, dx\\ &=\frac {65219}{128 (1-2 x)^2}-\frac {144837}{64 (1-2 x)}-\frac {5695 x}{4}-\frac {10425 x^2}{32}-\frac {375 x^3}{8}-\frac {64317}{32} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 47, normalized size = 0.90 \[ \frac {1}{32} \left (-\frac {2 \left (3000 x^5+17850 x^4+71020 x^3-137055 x^2+1509 x+15270\right )}{(1-2 x)^2}-64317 \log (1-2 x)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 57, normalized size = 1.10 \[ -\frac {24000 \, x^{5} + 142800 \, x^{4} + 568160 \, x^{3} - 687260 \, x^{2} + 257268 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 397108 \, x + 224455}{128 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 37, normalized size = 0.71 \[ -\frac {375}{8} \, x^{3} - \frac {10425}{32} \, x^{2} - \frac {5695}{4} \, x + \frac {847 \, {\left (684 \, x - 265\right )}}{128 \, {\left (2 \, x - 1\right )}^{2}} - \frac {64317}{32} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 41, normalized size = 0.79 \[ -\frac {375 x^{3}}{8}-\frac {10425 x^{2}}{32}-\frac {5695 x}{4}-\frac {64317 \ln \left (2 x -1\right )}{32}+\frac {65219}{128 \left (2 x -1\right )^{2}}+\frac {144837}{64 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 41, normalized size = 0.79 \[ -\frac {375}{8} \, x^{3} - \frac {10425}{32} \, x^{2} - \frac {5695}{4} \, x + \frac {847 \, {\left (684 \, x - 265\right )}}{128 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {64317}{32} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 36, normalized size = 0.69 \[ \frac {\frac {144837\,x}{128}-\frac {224455}{512}}{x^2-x+\frac {1}{4}}-\frac {64317\,\ln \left (x-\frac {1}{2}\right )}{32}-\frac {5695\,x}{4}-\frac {10425\,x^2}{32}-\frac {375\,x^3}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 44, normalized size = 0.85 \[ - \frac {375 x^{3}}{8} - \frac {10425 x^{2}}{32} - \frac {5695 x}{4} - \frac {224455 - 579348 x}{512 x^{2} - 512 x + 128} - \frac {64317 \log {\left (2 x - 1 \right )}}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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