Optimal. Leaf size=44 \[ -\frac {135 x^5}{2}-\frac {4995 x^4}{16}-\frac {5349 x^3}{8}-\frac {30175 x^2}{32}-\frac {39199 x}{32}-\frac {41503}{64} \log (1-2 x) \]
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Rubi [A] time = 0.02, antiderivative size = 44, 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} \[ -\frac {135 x^5}{2}-\frac {4995 x^4}{16}-\frac {5349 x^3}{8}-\frac {30175 x^2}{32}-\frac {39199 x}{32}-\frac {41503}{64} \log (1-2 x) \]
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} \, dx &=\int \left (-\frac {39199}{32}-\frac {30175 x}{16}-\frac {16047 x^2}{8}-\frac {4995 x^3}{4}-\frac {675 x^4}{2}-\frac {41503}{32 (-1+2 x)}\right ) \, dx\\ &=-\frac {39199 x}{32}-\frac {30175 x^2}{32}-\frac {5349 x^3}{8}-\frac {4995 x^4}{16}-\frac {135 x^5}{2}-\frac {41503}{64} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 37, normalized size = 0.84 \[ \frac {1}{256} \left (-17280 x^5-79920 x^4-171168 x^3-241400 x^2-313592 x-166012 \log (1-2 x)+244077\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 32, normalized size = 0.73 \[ -\frac {135}{2} \, x^{5} - \frac {4995}{16} \, x^{4} - \frac {5349}{8} \, x^{3} - \frac {30175}{32} \, x^{2} - \frac {39199}{32} \, x - \frac {41503}{64} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 33, normalized size = 0.75 \[ -\frac {135}{2} \, x^{5} - \frac {4995}{16} \, x^{4} - \frac {5349}{8} \, x^{3} - \frac {30175}{32} \, x^{2} - \frac {39199}{32} \, x - \frac {41503}{64} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 33, normalized size = 0.75 \[ -\frac {135 x^{5}}{2}-\frac {4995 x^{4}}{16}-\frac {5349 x^{3}}{8}-\frac {30175 x^{2}}{32}-\frac {39199 x}{32}-\frac {41503 \ln \left (2 x -1\right )}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 32, normalized size = 0.73 \[ -\frac {135}{2} \, x^{5} - \frac {4995}{16} \, x^{4} - \frac {5349}{8} \, x^{3} - \frac {30175}{32} \, x^{2} - \frac {39199}{32} \, x - \frac {41503}{64} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 30, normalized size = 0.68 \[ -\frac {39199\,x}{32}-\frac {41503\,\ln \left (x-\frac {1}{2}\right )}{64}-\frac {30175\,x^2}{32}-\frac {5349\,x^3}{8}-\frac {4995\,x^4}{16}-\frac {135\,x^5}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 42, normalized size = 0.95 \[ - \frac {135 x^{5}}{2} - \frac {4995 x^{4}}{16} - \frac {5349 x^{3}}{8} - \frac {30175 x^{2}}{32} - \frac {39199 x}{32} - \frac {41503 \log {\left (2 x - 1 \right )}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
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