Optimal. Leaf size=65 \[ -\frac {22148933 x}{256}-\frac {20766533 x^2}{256}-\frac {16987973 x^3}{192}-\frac {11088453 x^4}{128}-\frac {5333733 x^5}{80}-\frac {580815 x^6}{16}-\frac {342225 x^7}{28}-\frac {30375 x^8}{16}-\frac {22370117}{512} \log (1-2 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 65, 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 {30375 x^8}{16}-\frac {342225 x^7}{28}-\frac {580815 x^6}{16}-\frac {5333733 x^5}{80}-\frac {11088453 x^4}{128}-\frac {16987973 x^3}{192}-\frac {20766533 x^2}{256}-\frac {22148933 x}{256}-\frac {22370117}{512} \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)^5 (3+5 x)^3}{1-2 x} \, dx &=\int \left (-\frac {22148933}{256}-\frac {20766533 x}{128}-\frac {16987973 x^2}{64}-\frac {11088453 x^3}{32}-\frac {5333733 x^4}{16}-\frac {1742445 x^5}{8}-\frac {342225 x^6}{4}-\frac {30375 x^7}{2}-\frac {22370117}{256 (-1+2 x)}\right ) \, dx\\ &=-\frac {22148933 x}{256}-\frac {20766533 x^2}{256}-\frac {16987973 x^3}{192}-\frac {11088453 x^4}{128}-\frac {5333733 x^5}{80}-\frac {580815 x^6}{16}-\frac {342225 x^7}{28}-\frac {30375 x^8}{16}-\frac {22370117}{512} \log (1-2 x)\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 68, normalized size = 1.05 \begin {gather*} \frac {35596520969}{430080}-\frac {22148933 x}{256}-\frac {20766533 x^2}{256}-\frac {16987973 x^3}{192}-\frac {11088453 x^4}{128}-\frac {5333733 x^5}{80}-\frac {580815 x^6}{16}-\frac {342225 x^7}{28}-\frac {30375 x^8}{16}-\frac {22370117}{512} \log (1-2 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 48, normalized size = 0.74
method | result | size |
default | \(-\frac {30375 x^{8}}{16}-\frac {342225 x^{7}}{28}-\frac {580815 x^{6}}{16}-\frac {5333733 x^{5}}{80}-\frac {11088453 x^{4}}{128}-\frac {16987973 x^{3}}{192}-\frac {20766533 x^{2}}{256}-\frac {22148933 x}{256}-\frac {22370117 \ln \left (-1+2 x \right )}{512}\) | \(48\) |
norman | \(-\frac {30375 x^{8}}{16}-\frac {342225 x^{7}}{28}-\frac {580815 x^{6}}{16}-\frac {5333733 x^{5}}{80}-\frac {11088453 x^{4}}{128}-\frac {16987973 x^{3}}{192}-\frac {20766533 x^{2}}{256}-\frac {22148933 x}{256}-\frac {22370117 \ln \left (-1+2 x \right )}{512}\) | \(48\) |
risch | \(-\frac {30375 x^{8}}{16}-\frac {342225 x^{7}}{28}-\frac {580815 x^{6}}{16}-\frac {5333733 x^{5}}{80}-\frac {11088453 x^{4}}{128}-\frac {16987973 x^{3}}{192}-\frac {20766533 x^{2}}{256}-\frac {22148933 x}{256}-\frac {22370117 \ln \left (-1+2 x \right )}{512}\) | \(48\) |
meijerg | \(-\frac {22370117 \ln \left (1-2 x \right )}{512}-5400 x -2460 x \left (6 x +6\right )-\frac {23045 x \left (16 x^{2}+12 x +12\right )}{12}-\frac {11989 x \left (120 x^{3}+80 x^{2}+60 x +60\right )}{32}-\frac {149637 x \left (192 x^{4}+120 x^{3}+80 x^{2}+60 x +60\right )}{640}-\frac {23337 x \left (2240 x^{5}+1344 x^{4}+840 x^{3}+560 x^{2}+420 x +420\right )}{1792}-\frac {1485 x \left (7680 x^{6}+4480 x^{5}+2688 x^{4}+1680 x^{3}+1120 x^{2}+840 x +840\right )}{1024}-\frac {675 x \left (40320 x^{7}+23040 x^{6}+13440 x^{5}+8064 x^{4}+5040 x^{3}+3360 x^{2}+2520 x +2520\right )}{14336}\) | \(174\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 47, normalized size = 0.72 \begin {gather*} -\frac {30375}{16} \, x^{8} - \frac {342225}{28} \, x^{7} - \frac {580815}{16} \, x^{6} - \frac {5333733}{80} \, x^{5} - \frac {11088453}{128} \, x^{4} - \frac {16987973}{192} \, x^{3} - \frac {20766533}{256} \, x^{2} - \frac {22148933}{256} \, x - \frac {22370117}{512} \, \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 = 1.18, size = 47, normalized size = 0.72 \begin {gather*} -\frac {30375}{16} \, x^{8} - \frac {342225}{28} \, x^{7} - \frac {580815}{16} \, x^{6} - \frac {5333733}{80} \, x^{5} - \frac {11088453}{128} \, x^{4} - \frac {16987973}{192} \, x^{3} - \frac {20766533}{256} \, x^{2} - \frac {22148933}{256} \, x - \frac {22370117}{512} \, \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 = 0.08, size = 63, normalized size = 0.97 \begin {gather*} - \frac {30375 x^{8}}{16} - \frac {342225 x^{7}}{28} - \frac {580815 x^{6}}{16} - \frac {5333733 x^{5}}{80} - \frac {11088453 x^{4}}{128} - \frac {16987973 x^{3}}{192} - \frac {20766533 x^{2}}{256} - \frac {22148933 x}{256} - \frac {22370117 \log {\left (2 x - 1 \right )}}{512} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.75, size = 48, normalized size = 0.74 \begin {gather*} -\frac {30375}{16} \, x^{8} - \frac {342225}{28} \, x^{7} - \frac {580815}{16} \, x^{6} - \frac {5333733}{80} \, x^{5} - \frac {11088453}{128} \, x^{4} - \frac {16987973}{192} \, x^{3} - \frac {20766533}{256} \, x^{2} - \frac {22148933}{256} \, x - \frac {22370117}{512} \, \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 = 0.04, size = 45, normalized size = 0.69 \begin {gather*} -\frac {22148933\,x}{256}-\frac {22370117\,\ln \left (x-\frac {1}{2}\right )}{512}-\frac {20766533\,x^2}{256}-\frac {16987973\,x^3}{192}-\frac {11088453\,x^4}{128}-\frac {5333733\,x^5}{80}-\frac {580815\,x^6}{16}-\frac {342225\,x^7}{28}-\frac {30375\,x^8}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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