Optimal. Leaf size=58 \[ -\frac {729 x^4}{200}-\frac {8019 x^3}{500}-\frac {335097 x^2}{10000}-\frac {2682909 x}{50000}-\frac {1}{171875 (5 x+3)}-\frac {117649 \log (1-2 x)}{3872}+\frac {8 \log (5 x+3)}{75625} \]
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Rubi [A] time = 0.03, antiderivative size = 58, 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} \[ -\frac {729 x^4}{200}-\frac {8019 x^3}{500}-\frac {335097 x^2}{10000}-\frac {2682909 x}{50000}-\frac {1}{171875 (5 x+3)}-\frac {117649 \log (1-2 x)}{3872}+\frac {8 \log (5 x+3)}{75625} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(2+3 x)^6}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac {2682909}{50000}-\frac {335097 x}{5000}-\frac {24057 x^2}{500}-\frac {729 x^3}{50}-\frac {117649}{1936 (-1+2 x)}+\frac {1}{34375 (3+5 x)^2}+\frac {8}{15125 (3+5 x)}\right ) \, dx\\ &=-\frac {2682909 x}{50000}-\frac {335097 x^2}{10000}-\frac {8019 x^3}{500}-\frac {729 x^4}{200}-\frac {1}{171875 (3+5 x)}-\frac {117649 \log (1-2 x)}{3872}+\frac {8 \log (3+5 x)}{75625}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 54, normalized size = 0.93 \[ \frac {-80190000 x^4-352836000 x^3-737213400 x^2-1180479960 x-\frac {128}{5 x+3}+823659705}{22000000}-\frac {117649 \log (1-2 x)}{3872}+\frac {8 \log (10 x+6)}{75625} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.05, size = 60, normalized size = 1.03 \[ -\frac {1102612500 \, x^{5} + 5513062500 \, x^{4} + 13047581250 \, x^{3} + 22313610000 \, x^{2} - 6400 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 1838265625 \, {\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 9738959670 \, x + 352}{60500000 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 81, normalized size = 1.40 \[ -\frac {27}{250000} \, {\left (5 \, x + 3\right )}^{4} {\left (\frac {540}{5 \, x + 3} + \frac {4635}{{\left (5 \, x + 3\right )}^{2}} + \frac {51145}{{\left (5 \, x + 3\right )}^{3}} + 54\right )} - \frac {1}{171875 \, {\left (5 \, x + 3\right )}} + \frac {607689}{20000} \, \log \left (\frac {{\left | 5 \, x + 3 \right |}}{5 \, {\left (5 \, x + 3\right )}^{2}}\right ) - \frac {117649}{3872} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 45, normalized size = 0.78 \[ -\frac {729 x^{4}}{200}-\frac {8019 x^{3}}{500}-\frac {335097 x^{2}}{10000}-\frac {2682909 x}{50000}-\frac {117649 \ln \left (2 x -1\right )}{3872}+\frac {8 \ln \left (5 x +3\right )}{75625}-\frac {1}{171875 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 44, normalized size = 0.76 \[ -\frac {729}{200} \, x^{4} - \frac {8019}{500} \, x^{3} - \frac {335097}{10000} \, x^{2} - \frac {2682909}{50000} \, x - \frac {1}{171875 \, {\left (5 \, x + 3\right )}} + \frac {8}{75625} \, \log \left (5 \, x + 3\right ) - \frac {117649}{3872} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 40, normalized size = 0.69 \[ \frac {8\,\ln \left (x+\frac {3}{5}\right )}{75625}-\frac {117649\,\ln \left (x-\frac {1}{2}\right )}{3872}-\frac {2682909\,x}{50000}-\frac {1}{859375\,\left (x+\frac {3}{5}\right )}-\frac {335097\,x^2}{10000}-\frac {8019\,x^3}{500}-\frac {729\,x^4}{200} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 51, normalized size = 0.88 \[ - \frac {729 x^{4}}{200} - \frac {8019 x^{3}}{500} - \frac {335097 x^{2}}{10000} - \frac {2682909 x}{50000} - \frac {117649 \log {\left (x - \frac {1}{2} \right )}}{3872} + \frac {8 \log {\left (x + \frac {3}{5} \right )}}{75625} - \frac {1}{859375 x + 515625} \]
Verification of antiderivative is not currently implemented for this CAS.
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