Optimal. Leaf size=51 \[ -\frac {281305 x}{64}-\frac {238297 x^2}{64}-\frac {51571 x^3}{16}-\frac {68121 x^4}{32}-\frac {3537 x^5}{4}-\frac {675 x^6}{4}-\frac {290521}{128} \log (1-2 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 51, 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 = {90}
\begin {gather*} -\frac {675 x^6}{4}-\frac {3537 x^5}{4}-\frac {68121 x^4}{32}-\frac {51571 x^3}{16}-\frac {238297 x^2}{64}-\frac {281305 x}{64}-\frac {290521}{128} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^4 (3+5 x)^2}{1-2 x} \, dx &=\int \left (-\frac {281305}{64}-\frac {238297 x}{32}-\frac {154713 x^2}{16}-\frac {68121 x^3}{8}-\frac {17685 x^4}{4}-\frac {2025 x^5}{2}-\frac {290521}{64 (-1+2 x)}\right ) \, dx\\ &=-\frac {281305 x}{64}-\frac {238297 x^2}{64}-\frac {51571 x^3}{16}-\frac {68121 x^4}{32}-\frac {3537 x^5}{4}-\frac {675 x^6}{4}-\frac {290521}{128} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 42, normalized size = 0.82 \begin {gather*} \frac {1}{512} \left (1891717-2250440 x-1906376 x^2-1650272 x^3-1089936 x^4-452736 x^5-86400 x^6-1162084 \log (1-2 x)\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 38, normalized size = 0.75
method | result | size |
default | \(-\frac {675 x^{6}}{4}-\frac {3537 x^{5}}{4}-\frac {68121 x^{4}}{32}-\frac {51571 x^{3}}{16}-\frac {238297 x^{2}}{64}-\frac {281305 x}{64}-\frac {290521 \ln \left (-1+2 x \right )}{128}\) | \(38\) |
norman | \(-\frac {675 x^{6}}{4}-\frac {3537 x^{5}}{4}-\frac {68121 x^{4}}{32}-\frac {51571 x^{3}}{16}-\frac {238297 x^{2}}{64}-\frac {281305 x}{64}-\frac {290521 \ln \left (-1+2 x \right )}{128}\) | \(38\) |
risch | \(-\frac {675 x^{6}}{4}-\frac {3537 x^{5}}{4}-\frac {68121 x^{4}}{32}-\frac {51571 x^{3}}{16}-\frac {238297 x^{2}}{64}-\frac {281305 x}{64}-\frac {290521 \ln \left (-1+2 x \right )}{128}\) | \(38\) |
meijerg | \(-\frac {290521 \ln \left (1-2 x \right )}{128}-672 x -\frac {653 x \left (6 x +6\right )}{3}-\frac {451 x \left (16 x^{2}+12 x +12\right )}{4}-\frac {4203 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{320}-\frac {261 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{64}-\frac {135 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{1792}\) | \(103\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 37, normalized size = 0.73 \begin {gather*} -\frac {675}{4} \, x^{6} - \frac {3537}{4} \, x^{5} - \frac {68121}{32} \, x^{4} - \frac {51571}{16} \, x^{3} - \frac {238297}{64} \, x^{2} - \frac {281305}{64} \, x - \frac {290521}{128} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.78, size = 37, normalized size = 0.73 \begin {gather*} -\frac {675}{4} \, x^{6} - \frac {3537}{4} \, x^{5} - \frac {68121}{32} \, x^{4} - \frac {51571}{16} \, x^{3} - \frac {238297}{64} \, x^{2} - \frac {281305}{64} \, x - \frac {290521}{128} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 49, normalized size = 0.96 \begin {gather*} - \frac {675 x^{6}}{4} - \frac {3537 x^{5}}{4} - \frac {68121 x^{4}}{32} - \frac {51571 x^{3}}{16} - \frac {238297 x^{2}}{64} - \frac {281305 x}{64} - \frac {290521 \log {\left (2 x - 1 \right )}}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.85, size = 38, normalized size = 0.75 \begin {gather*} -\frac {675}{4} \, x^{6} - \frac {3537}{4} \, x^{5} - \frac {68121}{32} \, x^{4} - \frac {51571}{16} \, x^{3} - \frac {238297}{64} \, x^{2} - \frac {281305}{64} \, x - \frac {290521}{128} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 35, normalized size = 0.69 \begin {gather*} -\frac {281305\,x}{64}-\frac {290521\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {238297\,x^2}{64}-\frac {51571\,x^3}{16}-\frac {68121\,x^4}{32}-\frac {3537\,x^5}{4}-\frac {675\,x^6}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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