Optimal. Leaf size=53 \[ \frac {136}{5929 (1-2 x)}+\frac {1}{77 (1-2 x)^2}-\frac {6938 \log (1-2 x)}{456533}-\frac {27}{343} \log (3 x+2)+\frac {125 \log (5 x+3)}{1331} \]
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Rubi [A] time = 0.02, antiderivative size = 53, 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 = {72} \[ \frac {136}{5929 (1-2 x)}+\frac {1}{77 (1-2 x)^2}-\frac {6938 \log (1-2 x)}{456533}-\frac {27}{343} \log (3 x+2)+\frac {125 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^3 (2+3 x) (3+5 x)} \, dx &=\int \left (-\frac {4}{77 (-1+2 x)^3}+\frac {272}{5929 (-1+2 x)^2}-\frac {13876}{456533 (-1+2 x)}-\frac {81}{343 (2+3 x)}+\frac {625}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {1}{77 (1-2 x)^2}+\frac {136}{5929 (1-2 x)}-\frac {6938 \log (1-2 x)}{456533}-\frac {27}{343} \log (2+3 x)+\frac {125 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 52, normalized size = 0.98 \[ \frac {-6938 \log (3-6 x)-35937 \log (3 x+2)+\frac {7 \left (-2992 x+6125 (1-2 x)^2 \log (-3 (5 x+3))+2343\right )}{(1-2 x)^2}}{456533} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 73, normalized size = 1.38 \[ \frac {42875 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) - 35937 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) - 6938 \, {\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 20944 \, x + 16401}{456533 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.15, size = 42, normalized size = 0.79 \[ -\frac {272 \, x - 213}{5929 \, {\left (2 \, x - 1\right )}^{2}} + \frac {125}{1331} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {27}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {6938}{456533} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 44, normalized size = 0.83 \[ -\frac {6938 \ln \left (2 x -1\right )}{456533}-\frac {27 \ln \left (3 x +2\right )}{343}+\frac {125 \ln \left (5 x +3\right )}{1331}+\frac {1}{77 \left (2 x -1\right )^{2}}-\frac {136}{5929 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 44, normalized size = 0.83 \[ -\frac {272 \, x - 213}{5929 \, {\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac {125}{1331} \, \log \left (5 \, x + 3\right ) - \frac {27}{343} \, \log \left (3 \, x + 2\right ) - \frac {6938}{456533} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 36, normalized size = 0.68 \[ \frac {125\,\ln \left (x+\frac {3}{5}\right )}{1331}-\frac {27\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {6938\,\ln \left (x-\frac {1}{2}\right )}{456533}-\frac {\frac {68\,x}{5929}-\frac {213}{23716}}{x^2-x+\frac {1}{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 44, normalized size = 0.83 \[ - \frac {272 x - 213}{23716 x^{2} - 23716 x + 5929} - \frac {6938 \log {\left (x - \frac {1}{2} \right )}}{456533} + \frac {125 \log {\left (x + \frac {3}{5} \right )}}{1331} - \frac {27 \log {\left (x + \frac {2}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
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