Optimal. Leaf size=73 \[ -\frac {6075 x^6}{16}-\frac {48843 x^5}{16}-\frac {770067 x^4}{64}-\frac {1024389 x^3}{32}-\frac {17700255 x^2}{256}-\frac {39980457 x}{256}-\frac {12386759}{128 (1-2 x)}+\frac {14235529}{1024 (1-2 x)^2}-\frac {18859855}{128} \log (1-2 x) \]
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Rubi [A] time = 0.04, antiderivative size = 73, 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} \[ -\frac {6075 x^6}{16}-\frac {48843 x^5}{16}-\frac {770067 x^4}{64}-\frac {1024389 x^3}{32}-\frac {17700255 x^2}{256}-\frac {39980457 x}{256}-\frac {12386759}{128 (1-2 x)}+\frac {14235529}{1024 (1-2 x)^2}-\frac {18859855}{128} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^6 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac {39980457}{256}-\frac {17700255 x}{128}-\frac {3073167 x^2}{32}-\frac {770067 x^3}{16}-\frac {244215 x^4}{16}-\frac {18225 x^5}{8}-\frac {14235529}{256 (-1+2 x)^3}-\frac {12386759}{64 (-1+2 x)^2}-\frac {18859855}{64 (-1+2 x)}\right ) \, dx\\ &=\frac {14235529}{1024 (1-2 x)^2}-\frac {12386759}{128 (1-2 x)}-\frac {39980457 x}{256}-\frac {17700255 x^2}{256}-\frac {1024389 x^3}{32}-\frac {770067 x^4}{64}-\frac {48843 x^5}{16}-\frac {6075 x^6}{16}-\frac {18859855}{128} \log (1-2 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 66, normalized size = 0.90 \[ -\frac {777600 x^8+5474304 x^7+18584640 x^6+42481728 x^5+82201680 x^4+194631840 x^3-489708252 x^2+186131948 x+75439420 (1-2 x)^2 \log (1-2 x)-8887005}{512 (1-2 x)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 72, normalized size = 0.99 \[ -\frac {1555200 \, x^{8} + 10948608 \, x^{7} + 37169280 \, x^{6} + 84963456 \, x^{5} + 164403360 \, x^{4} + 389263680 \, x^{3} - 568886292 \, x^{2} + 150878840 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 38266316 \, x + 84858543}{1024 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 52, normalized size = 0.71 \[ -\frac {6075}{16} \, x^{6} - \frac {48843}{16} \, x^{5} - \frac {770067}{64} \, x^{4} - \frac {1024389}{32} \, x^{3} - \frac {17700255}{256} \, x^{2} - \frac {39980457}{256} \, x + \frac {184877 \, {\left (1072 \, x - 459\right )}}{1024 \, {\left (2 \, x - 1\right )}^{2}} - \frac {18859855}{128} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 56, normalized size = 0.77 \[ -\frac {6075 x^{6}}{16}-\frac {48843 x^{5}}{16}-\frac {770067 x^{4}}{64}-\frac {1024389 x^{3}}{32}-\frac {17700255 x^{2}}{256}-\frac {39980457 x}{256}-\frac {18859855 \ln \left (2 x -1\right )}{128}+\frac {14235529}{1024 \left (2 x -1\right )^{2}}+\frac {12386759}{128 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 56, normalized size = 0.77 \[ -\frac {6075}{16} \, x^{6} - \frac {48843}{16} \, x^{5} - \frac {770067}{64} \, x^{4} - \frac {1024389}{32} \, x^{3} - \frac {17700255}{256} \, x^{2} - \frac {39980457}{256} \, x + \frac {184877 \, {\left (1072 \, x - 459\right )}}{1024 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac {18859855}{128} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 51, normalized size = 0.70 \[ \frac {\frac {12386759\,x}{256}-\frac {84858543}{4096}}{x^2-x+\frac {1}{4}}-\frac {18859855\,\ln \left (x-\frac {1}{2}\right )}{128}-\frac {39980457\,x}{256}-\frac {17700255\,x^2}{256}-\frac {1024389\,x^3}{32}-\frac {770067\,x^4}{64}-\frac {48843\,x^5}{16}-\frac {6075\,x^6}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 65, normalized size = 0.89 \[ - \frac {6075 x^{6}}{16} - \frac {48843 x^{5}}{16} - \frac {770067 x^{4}}{64} - \frac {1024389 x^{3}}{32} - \frac {17700255 x^{2}}{256} - \frac {39980457 x}{256} - \frac {84858543 - 198188144 x}{4096 x^{2} - 4096 x + 1024} - \frac {18859855 \log {\left (2 x - 1 \right )}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
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