Optimal. Leaf size=76 \[ \frac {91125 x^8}{32}+\frac {309825 x^7}{14}+\frac {2611845 x^6}{32}+\frac {15403257 x^5}{80}+\frac {85406805 x^4}{256}+\frac {7530189 x^3}{16}+\frac {310976027 x^2}{512}+\frac {230244479 x}{256}+\frac {156590819}{1024 (1-2 x)}+\frac {616195041 \log (1-2 x)}{1024} \]
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Rubi [A] time = 0.04, antiderivative size = 76, 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} \[ \frac {91125 x^8}{32}+\frac {309825 x^7}{14}+\frac {2611845 x^6}{32}+\frac {15403257 x^5}{80}+\frac {85406805 x^4}{256}+\frac {7530189 x^3}{16}+\frac {310976027 x^2}{512}+\frac {230244479 x}{256}+\frac {156590819}{1024 (1-2 x)}+\frac {616195041 \log (1-2 x)}{1024} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^6 (3+5 x)^3}{(1-2 x)^2} \, dx &=\int \left (\frac {230244479}{256}+\frac {310976027 x}{256}+\frac {22590567 x^2}{16}+\frac {85406805 x^3}{64}+\frac {15403257 x^4}{16}+\frac {7835535 x^5}{16}+\frac {309825 x^6}{2}+\frac {91125 x^7}{4}+\frac {156590819}{512 (-1+2 x)^2}+\frac {616195041}{512 (-1+2 x)}\right ) \, dx\\ &=\frac {156590819}{1024 (1-2 x)}+\frac {230244479 x}{256}+\frac {310976027 x^2}{512}+\frac {7530189 x^3}{16}+\frac {85406805 x^4}{256}+\frac {15403257 x^5}{80}+\frac {2611845 x^6}{32}+\frac {309825 x^7}{14}+\frac {91125 x^8}{32}+\frac {616195041 \log (1-2 x)}{1024}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 69, normalized size = 0.91 \[ \frac {1632960000 x^9+11873952000 x^8+40459046400 x^7+87008414976 x^6+136105970112 x^5+174226352160 x^4+213352163360 x^3+341601057840 x^2-652800288858 x+172534611480 (2 x-1) \log (1-2 x)+153617806869}{286720 (2 x-1)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 67, normalized size = 0.88 \[ \frac {204120000 \, x^{9} + 1484244000 \, x^{8} + 5057380800 \, x^{7} + 10876051872 \, x^{6} + 17013246264 \, x^{5} + 21778294020 \, x^{4} + 26669020420 \, x^{3} + 42700132230 \, x^{2} + 21566826435 \, {\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 32234227060 \, x - 5480678665}{35840 \, {\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 102, normalized size = 1.34 \[ \frac {1}{286720} \, {\left (2 \, x - 1\right )}^{8} {\left (\frac {75087000}{2 \, x - 1} + \frac {801964800}{{\left (2 \, x - 1\right )}^{2}} + \frac {5138731584}{{\left (2 \, x - 1\right )}^{3}} + \frac {22047451020}{{\left (2 \, x - 1\right )}^{4}} + \frac {67259967600}{{\left (2 \, x - 1\right )}^{5}} + \frac {153877208800}{{\left (2 \, x - 1\right )}^{6}} + \frac {301719264000}{{\left (2 \, x - 1\right )}^{7}} + 3189375\right )} - \frac {156590819}{1024 \, {\left (2 \, x - 1\right )}} - \frac {616195041}{1024} \, \log \left (\frac {{\left | 2 \, x - 1 \right |}}{2 \, {\left (2 \, x - 1\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 57, normalized size = 0.75 \[ \frac {91125 x^{8}}{32}+\frac {309825 x^{7}}{14}+\frac {2611845 x^{6}}{32}+\frac {15403257 x^{5}}{80}+\frac {85406805 x^{4}}{256}+\frac {7530189 x^{3}}{16}+\frac {310976027 x^{2}}{512}+\frac {230244479 x}{256}+\frac {616195041 \ln \left (2 x -1\right )}{1024}-\frac {156590819}{1024 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.72, size = 56, normalized size = 0.74 \[ \frac {91125}{32} \, x^{8} + \frac {309825}{14} \, x^{7} + \frac {2611845}{32} \, x^{6} + \frac {15403257}{80} \, x^{5} + \frac {85406805}{256} \, x^{4} + \frac {7530189}{16} \, x^{3} + \frac {310976027}{512} \, x^{2} + \frac {230244479}{256} \, x - \frac {156590819}{1024 \, {\left (2 \, x - 1\right )}} + \frac {616195041}{1024} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 54, normalized size = 0.71 \[ \frac {230244479\,x}{256}+\frac {616195041\,\ln \left (x-\frac {1}{2}\right )}{1024}-\frac {156590819}{2048\,\left (x-\frac {1}{2}\right )}+\frac {310976027\,x^2}{512}+\frac {7530189\,x^3}{16}+\frac {85406805\,x^4}{256}+\frac {15403257\,x^5}{80}+\frac {2611845\,x^6}{32}+\frac {309825\,x^7}{14}+\frac {91125\,x^8}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 68, normalized size = 0.89 \[ \frac {91125 x^{8}}{32} + \frac {309825 x^{7}}{14} + \frac {2611845 x^{6}}{32} + \frac {15403257 x^{5}}{80} + \frac {85406805 x^{4}}{256} + \frac {7530189 x^{3}}{16} + \frac {310976027 x^{2}}{512} + \frac {230244479 x}{256} + \frac {616195041 \log {\left (2 x - 1 \right )}}{1024} - \frac {156590819}{2048 x - 1024} \]
Verification of antiderivative is not currently implemented for this CAS.
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