Optimal. Leaf size=53 \[ \frac {4}{539 (1-2 x)}+\frac {9}{49 (3 x+2)}-\frac {404 \log (1-2 x)}{41503}-\frac {351}{343} \log (3 x+2)+\frac {125}{121} \log (5 x+3) \]
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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 = {88} \[ \frac {4}{539 (1-2 x)}+\frac {9}{49 (3 x+2)}-\frac {404 \log (1-2 x)}{41503}-\frac {351}{343} \log (3 x+2)+\frac {125}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)} \, dx &=\int \left (\frac {8}{539 (-1+2 x)^2}-\frac {808}{41503 (-1+2 x)}-\frac {27}{49 (2+3 x)^2}-\frac {1053}{343 (2+3 x)}+\frac {625}{121 (3+5 x)}\right ) \, dx\\ &=\frac {4}{539 (1-2 x)}+\frac {9}{49 (2+3 x)}-\frac {404 \log (1-2 x)}{41503}-\frac {351}{343} \log (2+3 x)+\frac {125}{121} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 56, normalized size = 1.06 \[ \frac {\frac {14322 x}{6 x^2+x-2}-\frac {8239}{6 x^2+x-2}-404 \log (5-10 x)-42471 \log (5 (3 x+2))+42875 \log (5 x+3)}{41503} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 65, normalized size = 1.23 \[ \frac {42875 \, {\left (6 \, x^{2} + x - 2\right )} \log \left (5 \, x + 3\right ) - 42471 \, {\left (6 \, x^{2} + x - 2\right )} \log \left (3 \, x + 2\right ) - 404 \, {\left (6 \, x^{2} + x - 2\right )} \log \left (2 \, x - 1\right ) + 14322 \, x - 8239}{41503 \, {\left (6 \, x^{2} + x - 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.21, size = 55, normalized size = 1.04 \[ \frac {9}{49 \, {\left (3 \, x + 2\right )}} + \frac {24}{3773 \, {\left (\frac {7}{3 \, x + 2} - 2\right )}} + \frac {125}{121} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {404}{41503} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \]
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 \[ -\frac {404 \ln \left (2 x -1\right )}{41503}-\frac {351 \ln \left (3 x +2\right )}{343}+\frac {125 \ln \left (5 x +3\right )}{121}+\frac {9}{49 \left (3 x +2\right )}-\frac {4}{539 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 42, normalized size = 0.79 \[ \frac {186 \, x - 107}{539 \, {\left (6 \, x^{2} + x - 2\right )}} + \frac {125}{121} \, \log \left (5 \, x + 3\right ) - \frac {351}{343} \, \log \left (3 \, x + 2\right ) - \frac {404}{41503} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 0.66 \[ \frac {125\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {351\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {404\,\ln \left (x-\frac {1}{2}\right )}{41503}+\frac {\frac {31\,x}{539}-\frac {107}{3234}}{x^2+\frac {x}{6}-\frac {1}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 44, normalized size = 0.83 \[ \frac {186 x - 107}{3234 x^{2} + 539 x - 1078} - \frac {404 \log {\left (x - \frac {1}{2} \right )}}{41503} + \frac {125 \log {\left (x + \frac {3}{5} \right )}}{121} - \frac {351 \log {\left (x + \frac {2}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
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