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 = 0.02, antiderivative size = 48, 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} \[ \frac {675 x^4}{16}+\frac {945 x^3}{4}+\frac {21717 x^2}{32}+\frac {12973 x}{8}+\frac {41503}{64 (1-2 x)}+\frac {91091}{64} \log (1-2 x) \]
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*}
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Mathematica [A] time = 0.02, 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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fricas [A] time = 0.69, size = 47, normalized size = 0.98 \[ \frac {5400 \, x^{5} + 27540 \, x^{4} + 71748 \, x^{3} + 164134 \, x^{2} + 91091 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 103784 \, x - 41503}{64 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.85, size = 66, normalized size = 1.38 \[ \frac {1}{256} \, {\left (2 \, x - 1\right )}^{4} {\left (\frac {10260}{2 \, x - 1} + \frac {70164}{{\left (2 \, x - 1\right )}^{2}} + \frac {319816}{{\left (2 \, x - 1\right )}^{3}} + 675\right )} - \frac {41503}{64 \, {\left (2 \, x - 1\right )}} - \frac {91091}{64} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 37, normalized size = 0.77 \[ \frac {675 x^{4}}{16}+\frac {945 x^{3}}{4}+\frac {21717 x^{2}}{32}+\frac {12973 x}{8}+\frac {91091 \ln \left (2 x -1\right )}{64}-\frac {41503}{64 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 36, normalized size = 0.75 \[ \frac {675}{16} \, x^{4} + \frac {945}{4} \, x^{3} + \frac {21717}{32} \, x^{2} + \frac {12973}{8} \, x - \frac {41503}{64 \, {\left (2 \, x - 1\right )}} + \frac {91091}{64} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 34, normalized size = 0.71 \[ \frac {12973\,x}{8}+\frac {91091\,\ln \left (x-\frac {1}{2}\right )}{64}-\frac {41503}{128\,\left (x-\frac {1}{2}\right )}+\frac {21717\,x^2}{32}+\frac {945\,x^3}{4}+\frac {675\,x^4}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 41, normalized size = 0.85 \[ \frac {675 x^{4}}{16} + \frac {945 x^{3}}{4} + \frac {21717 x^{2}}{32} + \frac {12973 x}{8} + \frac {91091 \log {\left (2 x - 1 \right )}}{64} - \frac {41503}{128 x - 64} \]
Verification of antiderivative is not currently implemented for this CAS.
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