Optimal. Leaf size=44 \[ -\frac {81 x^5}{2}-\frac {3051 x^4}{16}-\frac {3321 x^3}{8}-\frac {18987 x^2}{32}-\frac {24875 x}{32}-\frac {26411}{64} \log (1-2 x) \]
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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 = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \begin {gather*} -\frac {81 x^5}{2}-\frac {3051 x^4}{16}-\frac {3321 x^3}{8}-\frac {18987 x^2}{32}-\frac {24875 x}{32}-\frac {26411}{64} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac {24875}{32}-\frac {18987 x}{16}-\frac {9963 x^2}{8}-\frac {3051 x^3}{4}-\frac {405 x^4}{2}-\frac {26411}{32 (-1+2 x)}\right ) \, dx\\ &=-\frac {24875 x}{32}-\frac {18987 x^2}{32}-\frac {3321 x^3}{8}-\frac {3051 x^4}{16}-\frac {81 x^5}{2}-\frac {26411}{64} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 37, normalized size = 0.84 \begin {gather*} \frac {1}{256} \left (-10368 x^5-48816 x^4-106272 x^3-151896 x^2-199000 x-105644 \log (1-2 x)+154133\right ) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(2+3 x)^4 (3+5 x)}{1-2 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.03, size = 32, normalized size = 0.73 \begin {gather*} -\frac {81}{2} \, x^{5} - \frac {3051}{16} \, x^{4} - \frac {3321}{8} \, x^{3} - \frac {18987}{32} \, x^{2} - \frac {24875}{32} \, x - \frac {26411}{64} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.04, size = 33, normalized size = 0.75 \begin {gather*} -\frac {81}{2} \, x^{5} - \frac {3051}{16} \, x^{4} - \frac {3321}{8} \, x^{3} - \frac {18987}{32} \, x^{2} - \frac {24875}{32} \, x - \frac {26411}{64} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
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 \begin {gather*} -\frac {81 x^{5}}{2}-\frac {3051 x^{4}}{16}-\frac {3321 x^{3}}{8}-\frac {18987 x^{2}}{32}-\frac {24875 x}{32}-\frac {26411 \ln \left (2 x -1\right )}{64} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 32, normalized size = 0.73 \begin {gather*} -\frac {81}{2} \, x^{5} - \frac {3051}{16} \, x^{4} - \frac {3321}{8} \, x^{3} - \frac {18987}{32} \, x^{2} - \frac {24875}{32} \, x - \frac {26411}{64} \, \log \left (2 \, x - 1\right ) \end {gather*}
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 \begin {gather*} -\frac {24875\,x}{32}-\frac {26411\,\ln \left (x-\frac {1}{2}\right )}{64}-\frac {18987\,x^2}{32}-\frac {3321\,x^3}{8}-\frac {3051\,x^4}{16}-\frac {81\,x^5}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 42, normalized size = 0.95 \begin {gather*} - \frac {81 x^{5}}{2} - \frac {3051 x^{4}}{16} - \frac {3321 x^{3}}{8} - \frac {18987 x^{2}}{32} - \frac {24875 x}{32} - \frac {26411 \log {\left (2 x - 1 \right )}}{64} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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