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 = 0.03, antiderivative size = 66, 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} \[ -\frac {729 x^2}{400}-\frac {31347 x}{2000}-\frac {67228}{1331 (1-2 x)}-\frac {1}{831875 (5 x+3)}+\frac {117649}{7744 (1-2 x)^2}-\frac {7383075 \log (1-2 x)}{234256}+\frac {204 \log (5 x+3)}{9150625} \]
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*}
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Mathematica [A] time = 0.05, 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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fricas [A] time = 0.57, size = 90, normalized size = 1.36 \[ -\frac {21346578000 \, x^{5} + 175041939600 \, x^{4} - 80903530620 \, x^{3} - 356854410264 \, x^{2} - 13056 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 18457687500 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 46529265321 \, x + 62049343829}{585640000 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.20, size = 94, normalized size = 1.42 \[ -\frac {{\left (5 \, x + 3\right )}^{2} {\left (\frac {555011028}{5 \, x + 3} - \frac {13845990449}{{\left (5 \, x + 3\right )}^{2}} + \frac {50757096489}{{\left (5 \, x + 3\right )}^{3}} + 21346578\right )}}{73205000 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}^{2}} - \frac {1}{831875 \, {\left (5 \, x + 3\right )}} + \frac {315171}{10000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {7383075}{234256} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 53, normalized size = 0.80 \[ -\frac {729 x^{2}}{400}-\frac {31347 x}{2000}-\frac {7383075 \ln \left (2 x -1\right )}{234256}+\frac {204 \ln \left (5 x +3\right )}{9150625}-\frac {1}{831875 \left (5 x +3\right )}+\frac {117649}{7744 \left (2 x -1\right )^{2}}+\frac {67228}{1331 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 54, normalized size = 0.82 \[ -\frac {729}{400} \, x^{2} - \frac {31347}{2000} \, x + \frac {26891199744 \, x^{2} + 6733304631 \, x - 5640849439}{53240000 \, {\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac {204}{9150625} \, \log \left (5 \, x + 3\right ) - \frac {7383075}{234256} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 50, normalized size = 0.76 \[ \frac {204\,\ln \left (x+\frac {3}{5}\right )}{9150625}-\frac {7383075\,\ln \left (x-\frac {1}{2}\right )}{234256}-\frac {31347\,x}{2000}-\frac {\frac {105043749\,x^2}{4159375}+\frac {6733304631\,x}{1064800000}-\frac {5640849439}{1064800000}}{-x^3+\frac {2\,x^2}{5}+\frac {7\,x}{20}-\frac {3}{20}}-\frac {729\,x^2}{400} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 56, normalized size = 0.85 \[ - \frac {729 x^{2}}{400} - \frac {31347 x}{2000} - \frac {- 26891199744 x^{2} - 6733304631 x + 5640849439}{1064800000 x^{3} - 425920000 x^{2} - 372680000 x + 159720000} - \frac {7383075 \log {\left (x - \frac {1}{2} \right )}}{234256} + \frac {204 \log {\left (x + \frac {3}{5} \right )}}{9150625} \]
Verification of antiderivative is not currently implemented for this CAS.
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