Optimal. Leaf size=76 \[ \frac {156590819}{1024 (1-2 x)}+\frac {230244479 x}{256}+\frac {310976027 x^2}{512}+\frac {7530189 x^3}{16}+\frac {85406805 x^4}{256}+\frac {15403257 x^5}{80}+\frac {2611845 x^6}{32}+\frac {309825 x^7}{14}+\frac {91125 x^8}{32}+\frac {616195041 \log (1-2 x)}{1024} \]
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Rubi [A]
time = 0.03, 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 = {90}
\begin {gather*} \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} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
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 = 0.01, size = 69, normalized size = 0.91 \begin {gather*} \frac {153617806869-652800288858 x+341601057840 x^2+213352163360 x^3+174226352160 x^4+136105970112 x^5+87008414976 x^6+40459046400 x^7+11873952000 x^8+1632960000 x^9+172534611480 (-1+2 x) \log (1-2 x)}{286720 (-1+2 x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 57, normalized size = 0.75
method | result | size |
risch | \(\frac {91125 x^{8}}{32}+\frac {309825 x^{7}}{14}+\frac {2611845 x^{6}}{32}+\frac {15403257 x^{5}}{80}+\frac {85406805 x^{4}}{256}+\frac {7530189 x^{3}}{16}+\frac {310976027 x^{2}}{512}+\frac {230244479 x}{256}-\frac {156590819}{2048 \left (-\frac {1}{2}+x \right )}+\frac {616195041 \ln \left (-1+2 x \right )}{1024}\) | \(55\) |
default | \(\frac {91125 x^{8}}{32}+\frac {309825 x^{7}}{14}+\frac {2611845 x^{6}}{32}+\frac {15403257 x^{5}}{80}+\frac {85406805 x^{4}}{256}+\frac {7530189 x^{3}}{16}+\frac {310976027 x^{2}}{512}+\frac {230244479 x}{256}-\frac {156590819}{1024 \left (-1+2 x \right )}+\frac {616195041 \ln \left (-1+2 x \right )}{1024}\) | \(57\) |
norman | \(\frac {-\frac {617079777}{512} x +\frac {610001889}{512} x^{2}+\frac {190493003}{256} x^{3}+\frac {155559243}{256} x^{4}+\frac {303807969}{640} x^{5}+\frac {48553803}{160} x^{6}+\frac {15804315}{112} x^{7}+\frac {9276525}{224} x^{8}+\frac {91125}{16} x^{9}}{-1+2 x}+\frac {616195041 \ln \left (-1+2 x \right )}{1024}\) | \(62\) |
meijerg | \(\frac {13824 x}{1-2 x}+\frac {18225 x \left (-8960 x^{8}-5760 x^{7}-3840 x^{6}-2688 x^{5}-2016 x^{4}-1680 x^{3}-1680 x^{2}-2520 x +2520\right )}{28672 \left (1-2 x \right )}+\frac {616195041 \ln \left (1-2 x \right )}{1024}+\frac {90801 x \left (-1280 x^{6}-896 x^{5}-672 x^{4}-560 x^{3}-560 x^{2}-840 x +840\right )}{1024 \left (1-2 x \right )}+\frac {11745 x \left (-5760 x^{7}-3840 x^{6}-2688 x^{5}-2016 x^{4}-1680 x^{3}-1680 x^{2}-2520 x +2520\right )}{1792 \left (1-2 x \right )}+\frac {2046843 x \left (-448 x^{5}-336 x^{4}-280 x^{3}-280 x^{2}-420 x +420\right )}{4480 \left (1-2 x \right )}+\frac {5148 x \left (-48 x^{4}-40 x^{3}-40 x^{2}-60 x +60\right )}{1-2 x}+\frac {34115 x \left (-8 x^{2}-12 x +12\right )}{2 \left (1-2 x \right )}+\frac {21207 x \left (-40 x^{3}-40 x^{2}-60 x +60\right )}{4 \left (1-2 x \right )}+\frac {12540 x \left (-6 x +6\right )}{1-2 x}\) | \(280\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 56, normalized size = 0.74 \begin {gather*} \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 ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.56, size = 67, normalized size = 0.88 \begin {gather*} \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 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 68, normalized size = 0.89 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.07, size = 102, normalized size = 1.34 \begin {gather*} \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 ) \end {gather*}
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 \begin {gather*} \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} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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