Optimal. Leaf size=72 \[ -\frac {3645 x^9}{2}-\frac {422091 x^8}{32}-\frac {353565 x^7}{8}-\frac {2929689 x^6}{32}-\frac {21272139 x^5}{160}-\frac {37722699 x^4}{256}-\frac {17391129 x^3}{128}-\frac {60332619 x^2}{512}-\frac {63019595 x}{512}-\frac {63412811 \log (1-2 x)}{1024} \]
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Rubi [A] time = 0.03, antiderivative size = 72, 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 {3645 x^9}{2}-\frac {422091 x^8}{32}-\frac {353565 x^7}{8}-\frac {2929689 x^6}{32}-\frac {21272139 x^5}{160}-\frac {37722699 x^4}{256}-\frac {17391129 x^3}{128}-\frac {60332619 x^2}{512}-\frac {63019595 x}{512}-\frac {63412811 \log (1-2 x)}{1024} \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^8 (3+5 x)}{1-2 x} \, dx &=\int \left (-\frac {63019595}{512}-\frac {60332619 x}{256}-\frac {52173387 x^2}{128}-\frac {37722699 x^3}{64}-\frac {21272139 x^4}{32}-\frac {8789067 x^5}{16}-\frac {2474955 x^6}{8}-\frac {422091 x^7}{4}-\frac {32805 x^8}{2}-\frac {63412811}{512 (-1+2 x)}\right ) \, dx\\ &=-\frac {63019595 x}{512}-\frac {60332619 x^2}{512}-\frac {17391129 x^3}{128}-\frac {37722699 x^4}{256}-\frac {21272139 x^5}{160}-\frac {2929689 x^6}{32}-\frac {353565 x^7}{8}-\frac {422091 x^8}{32}-\frac {3645 x^9}{2}-\frac {63412811 \log (1-2 x)}{1024}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 57, normalized size = 0.79 \begin {gather*} \frac {-74649600 x^9-540276480 x^8-1810252800 x^7-3750001920 x^6-5445667584 x^5-6035631840 x^4-5565161280 x^3-4826609520 x^2-5041567600 x-2536512440 \log (1-2 x)+5045478077}{40960} \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)^8 (3+5 x)}{1-2 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.07, size = 52, normalized size = 0.72 \begin {gather*} -\frac {3645}{2} \, x^{9} - \frac {422091}{32} \, x^{8} - \frac {353565}{8} \, x^{7} - \frac {2929689}{32} \, x^{6} - \frac {21272139}{160} \, x^{5} - \frac {37722699}{256} \, x^{4} - \frac {17391129}{128} \, x^{3} - \frac {60332619}{512} \, x^{2} - \frac {63019595}{512} \, x - \frac {63412811}{1024} \, \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 = 1.07, size = 53, normalized size = 0.74 \begin {gather*} -\frac {3645}{2} \, x^{9} - \frac {422091}{32} \, x^{8} - \frac {353565}{8} \, x^{7} - \frac {2929689}{32} \, x^{6} - \frac {21272139}{160} \, x^{5} - \frac {37722699}{256} \, x^{4} - \frac {17391129}{128} \, x^{3} - \frac {60332619}{512} \, x^{2} - \frac {63019595}{512} \, x - \frac {63412811}{1024} \, \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 = 53, normalized size = 0.74 \begin {gather*} -\frac {3645 x^{9}}{2}-\frac {422091 x^{8}}{32}-\frac {353565 x^{7}}{8}-\frac {2929689 x^{6}}{32}-\frac {21272139 x^{5}}{160}-\frac {37722699 x^{4}}{256}-\frac {17391129 x^{3}}{128}-\frac {60332619 x^{2}}{512}-\frac {63019595 x}{512}-\frac {63412811 \ln \left (2 x -1\right )}{1024} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 52, normalized size = 0.72 \begin {gather*} -\frac {3645}{2} \, x^{9} - \frac {422091}{32} \, x^{8} - \frac {353565}{8} \, x^{7} - \frac {2929689}{32} \, x^{6} - \frac {21272139}{160} \, x^{5} - \frac {37722699}{256} \, x^{4} - \frac {17391129}{128} \, x^{3} - \frac {60332619}{512} \, x^{2} - \frac {63019595}{512} \, x - \frac {63412811}{1024} \, \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 = 0.05, size = 50, normalized size = 0.69 \begin {gather*} -\frac {63019595\,x}{512}-\frac {63412811\,\ln \left (x-\frac {1}{2}\right )}{1024}-\frac {60332619\,x^2}{512}-\frac {17391129\,x^3}{128}-\frac {37722699\,x^4}{256}-\frac {21272139\,x^5}{160}-\frac {2929689\,x^6}{32}-\frac {353565\,x^7}{8}-\frac {422091\,x^8}{32}-\frac {3645\,x^9}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 70, normalized size = 0.97 \begin {gather*} - \frac {3645 x^{9}}{2} - \frac {422091 x^{8}}{32} - \frac {353565 x^{7}}{8} - \frac {2929689 x^{6}}{32} - \frac {21272139 x^{5}}{160} - \frac {37722699 x^{4}}{256} - \frac {17391129 x^{3}}{128} - \frac {60332619 x^{2}}{512} - \frac {63019595 x}{512} - \frac {63412811 \log {\left (2 x - 1 \right )}}{1024} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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