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 = 0.0399722, antiderivative size = 73, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0195891, size = 66, normalized size = 0.9 \[ -\frac{777600 x^8+5474304 x^7+18584640 x^6+42481728 x^5+82201680 x^4+194631840 x^3-489708252 x^2+186131948 x+75439420 (1-2 x)^2 \log (1-2 x)-8887005}{512 (1-2 x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 56, normalized size = 0.8 \begin{align*} -{\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}{256\,x-128}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02605, size = 76, normalized size = 1.04 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47557, size = 271, normalized size = 3.71 \begin{align*} -\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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.134232, size = 63, normalized size = 0.86 \begin{align*} - \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{198188144 x - 84858543}{4096 x^{2} - 4096 x + 1024} - \frac{18859855 \log{\left (2 x - 1 \right )}}{128} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.94568, size = 70, normalized size = 0.96 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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