Optimal. Leaf size=66 \[ -\frac{729 x^2}{400}-\frac{31347 x}{2000}-\frac{67228}{1331 (1-2 x)}-\frac{1}{831875 (5 x+3)}+\frac{117649}{7744 (1-2 x)^2}-\frac{7383075 \log (1-2 x)}{234256}+\frac{204 \log (5 x+3)}{9150625} \]
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Rubi [A] time = 0.0320095, antiderivative size = 66, 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} \[ -\frac{729 x^2}{400}-\frac{31347 x}{2000}-\frac{67228}{1331 (1-2 x)}-\frac{1}{831875 (5 x+3)}+\frac{117649}{7744 (1-2 x)^2}-\frac{7383075 \log (1-2 x)}{234256}+\frac{204 \log (5 x+3)}{9150625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^6}{(1-2 x)^3 (3+5 x)^2} \, dx &=\int \left (-\frac{31347}{2000}-\frac{729 x}{200}-\frac{117649}{1936 (-1+2 x)^3}-\frac{134456}{1331 (-1+2 x)^2}-\frac{7383075}{117128 (-1+2 x)}+\frac{1}{166375 (3+5 x)^2}+\frac{204}{1830125 (3+5 x)}\right ) \, dx\\ &=\frac{117649}{7744 (1-2 x)^2}-\frac{67228}{1331 (1-2 x)}-\frac{31347 x}{2000}-\frac{729 x^2}{400}-\frac{1}{831875 (3+5 x)}-\frac{7383075 \log (1-2 x)}{234256}+\frac{204 \log (3+5 x)}{9150625}\\ \end{align*}
Mathematica [A] time = 0.0372138, size = 74, normalized size = 1.12 \[ -\frac{729 (1-2 x)^2}{1600}+\frac{2187}{250} (1-2 x)+\frac{67228}{1331 (2 x-1)}-\frac{1}{831875 (5 x+3)}+\frac{117649}{7744 (1-2 x)^2}-\frac{7383075 \log (1-2 x)}{234256}+\frac{204 \log (10 x+6)}{9150625} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 53, normalized size = 0.8 \begin{align*} -{\frac{729\,{x}^{2}}{400}}-{\frac{31347\,x}{2000}}+{\frac{117649}{7744\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{67228}{2662\,x-1331}}-{\frac{7383075\,\ln \left ( 2\,x-1 \right ) }{234256}}-{\frac{1}{2495625+4159375\,x}}+{\frac{204\,\ln \left ( 3+5\,x \right ) }{9150625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.62146, size = 73, normalized size = 1.11 \begin{align*} -\frac{729}{400} \, x^{2} - \frac{31347}{2000} \, x + \frac{26891199744 \, x^{2} + 6733304631 \, x - 5640849439}{53240000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{204}{9150625} \, \log \left (5 \, x + 3\right ) - \frac{7383075}{234256} \, \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 = 1.52363, size = 333, normalized size = 5.05 \begin{align*} -\frac{21346578000 \, x^{5} + 175041939600 \, x^{4} - 80903530620 \, x^{3} - 356854410264 \, x^{2} - 13056 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 18457687500 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 46529265321 \, x + 62049343829}{585640000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.190832, size = 56, normalized size = 0.85 \begin{align*} - \frac{729 x^{2}}{400} - \frac{31347 x}{2000} + \frac{26891199744 x^{2} + 6733304631 x - 5640849439}{1064800000 x^{3} - 425920000 x^{2} - 372680000 x + 159720000} - \frac{7383075 \log{\left (x - \frac{1}{2} \right )}}{234256} + \frac{204 \log{\left (x + \frac{3}{5} \right )}}{9150625} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.36413, size = 127, normalized size = 1.92 \begin{align*} -\frac{{\left (5 \, x + 3\right )}^{2}{\left (\frac{555011028}{5 \, x + 3} - \frac{13845990449}{{\left (5 \, x + 3\right )}^{2}} + \frac{50757096489}{{\left (5 \, x + 3\right )}^{3}} + 21346578\right )}}{73205000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{1}{831875 \,{\left (5 \, x + 3\right )}} + \frac{315171}{10000} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{7383075}{234256} \, \log \left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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