Optimal. Leaf size=75 \[ \frac {1104}{717409 (1-2 x)}+\frac {3375}{14641 (5 x+3)}+\frac {4}{9317 (1-2 x)^2}-\frac {125}{2662 (5 x+3)^2}-\frac {95232 \log (1-2 x)}{55240493}-\frac {243}{343} \log (3 x+2)+\frac {114375 \log (5 x+3)}{161051} \]
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Rubi [A] time = 0.04, antiderivative size = 75, 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} \[ \frac {1104}{717409 (1-2 x)}+\frac {3375}{14641 (5 x+3)}+\frac {4}{9317 (1-2 x)^2}-\frac {125}{2662 (5 x+3)^2}-\frac {95232 \log (1-2 x)}{55240493}-\frac {243}{343} \log (3 x+2)+\frac {114375 \log (5 x+3)}{161051} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^3 (2+3 x) (3+5 x)^3} \, dx &=\int \left (-\frac {16}{9317 (-1+2 x)^3}+\frac {2208}{717409 (-1+2 x)^2}-\frac {190464}{55240493 (-1+2 x)}-\frac {729}{343 (2+3 x)}+\frac {625}{1331 (3+5 x)^3}-\frac {16875}{14641 (3+5 x)^2}+\frac {571875}{161051 (3+5 x)}\right ) \, dx\\ &=\frac {4}{9317 (1-2 x)^2}+\frac {1104}{717409 (1-2 x)}-\frac {125}{2662 (3+5 x)^2}+\frac {3375}{14641 (3+5 x)}-\frac {95232 \log (1-2 x)}{55240493}-\frac {243}{343} \log (2+3 x)+\frac {114375 \log (3+5 x)}{161051}\\ \end {align*}
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Mathematica [A] time = 0.09, size = 60, normalized size = 0.80 \[ -\frac {3 \left (-\frac {77 \left (6504600 x^3-2977380 x^2-2000774 x+950291\right )}{3 \left (10 x^2+x-3\right )^2}+63488 \log (3-6 x)+26090262 \log (3 x+2)-26153750 \log (-3 (5 x+3))\right )}{110480986} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.73, size = 123, normalized size = 1.64 \[ \frac {500854200 \, x^{3} - 229258260 \, x^{2} + 78461250 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 78270786 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (3 \, x + 2\right ) - 190464 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 154059598 \, x + 73172407}{110480986 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.26, size = 59, normalized size = 0.79 \[ \frac {6504600 \, x^{3} - 2977380 \, x^{2} - 2000774 \, x + 950291}{1434818 \, {\left (5 \, x + 3\right )}^{2} {\left (2 \, x - 1\right )}^{2}} + \frac {114375}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {243}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {95232}{55240493} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 62, normalized size = 0.83 \[ -\frac {95232 \ln \left (2 x -1\right )}{55240493}-\frac {243 \ln \left (3 x +2\right )}{343}+\frac {114375 \ln \left (5 x +3\right )}{161051}-\frac {125}{2662 \left (5 x +3\right )^{2}}+\frac {3375}{14641 \left (5 x +3\right )}+\frac {4}{9317 \left (2 x -1\right )^{2}}-\frac {1104}{717409 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 64, normalized size = 0.85 \[ \frac {6504600 \, x^{3} - 2977380 \, x^{2} - 2000774 \, x + 950291}{1434818 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {114375}{161051} \, \log \left (5 \, x + 3\right ) - \frac {243}{343} \, \log \left (3 \, x + 2\right ) - \frac {95232}{55240493} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 56, normalized size = 0.75 \[ \frac {114375\,\ln \left (x+\frac {3}{5}\right )}{161051}-\frac {243\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {95232\,\ln \left (x-\frac {1}{2}\right )}{55240493}-\frac {-\frac {32523\,x^3}{717409}+\frac {21267\,x^2}{1024870}+\frac {1000387\,x}{71740900}-\frac {950291}{143481800}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 65, normalized size = 0.87 \[ - \frac {- 6504600 x^{3} + 2977380 x^{2} + 2000774 x - 950291}{143481800 x^{4} + 28696360 x^{3} - 84654262 x^{2} - 8608908 x + 12913362} - \frac {95232 \log {\left (x - \frac {1}{2} \right )}}{55240493} + \frac {114375 \log {\left (x + \frac {3}{5} \right )}}{161051} - \frac {243 \log {\left (x + \frac {2}{3} \right )}}{343} \]
Verification of antiderivative is not currently implemented for this CAS.
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