Optimal. Leaf size=75 \[ \frac {16}{65219 (1-2 x)}+\frac {81}{49 (2+3 x)}-\frac {125}{242 (3+5 x)^2}+\frac {7750}{1331 (3+5 x)}-\frac {2736 \log (1-2 x)}{5021863}-\frac {8829}{343} \log (2+3 x)+\frac {376875 \log (3+5 x)}{14641} \]
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Rubi [A]
time = 0.03, 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 = {90}
\begin {gather*} \frac {16}{65219 (1-2 x)}+\frac {81}{49 (3 x+2)}+\frac {7750}{1331 (5 x+3)}-\frac {125}{242 (5 x+3)^2}-\frac {2736 \log (1-2 x)}{5021863}-\frac {8829}{343} \log (3 x+2)+\frac {376875 \log (5 x+3)}{14641} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^2 (2+3 x)^2 (3+5 x)^3} \, dx &=\int \left (\frac {32}{65219 (-1+2 x)^2}-\frac {5472}{5021863 (-1+2 x)}-\frac {243}{49 (2+3 x)^2}-\frac {26487}{343 (2+3 x)}+\frac {625}{121 (3+5 x)^3}-\frac {38750}{1331 (3+5 x)^2}+\frac {1884375}{14641 (3+5 x)}\right ) \, dx\\ &=\frac {16}{65219 (1-2 x)}+\frac {81}{49 (2+3 x)}-\frac {125}{242 (3+5 x)^2}+\frac {7750}{1331 (3+5 x)}-\frac {2736 \log (1-2 x)}{5021863}-\frac {8829}{343} \log (2+3 x)+\frac {376875 \log (3+5 x)}{14641}\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 65, normalized size = 0.87 \begin {gather*} \frac {\frac {77 \left (-6363424-7974123 x+24606540 x^2+33563700 x^3\right )}{(3+5 x)^2 \left (-2+x+6 x^2\right )}-5472 \log (5-10 x)-258530778 \log (5 (2+3 x))+258536250 \log (3+5 x)}{10043726} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 62, normalized size = 0.83
method | result | size |
default | \(-\frac {16}{65219 \left (-1+2 x \right )}-\frac {2736 \ln \left (-1+2 x \right )}{5021863}+\frac {81}{49 \left (2+3 x \right )}-\frac {8829 \ln \left (2+3 x \right )}{343}-\frac {125}{242 \left (3+5 x \right )^{2}}+\frac {7750}{1331 \left (3+5 x \right )}+\frac {376875 \ln \left (3+5 x \right )}{14641}\) | \(62\) |
risch | \(\frac {\frac {16781850}{65219} x^{3}+\frac {1757610}{9317} x^{2}-\frac {7974123}{130438} x -\frac {3181712}{65219}}{\left (-1+2 x \right ) \left (2+3 x \right ) \left (3+5 x \right )^{2}}-\frac {2736 \ln \left (-1+2 x \right )}{5021863}-\frac {8829 \ln \left (2+3 x \right )}{343}+\frac {376875 \ln \left (3+5 x \right )}{14641}\) | \(64\) |
norman | \(\frac {-\frac {25012690}{83853} x^{3}-\frac {79542800}{195657} x^{4}+\frac {56640326}{586971} x^{2}+\frac {30166735}{391314} x}{\left (-1+2 x \right ) \left (2+3 x \right ) \left (3+5 x \right )^{2}}-\frac {2736 \ln \left (-1+2 x \right )}{5021863}-\frac {8829 \ln \left (2+3 x \right )}{343}+\frac {376875 \ln \left (3+5 x \right )}{14641}\) | \(67\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.43, size = 64, normalized size = 0.85 \begin {gather*} \frac {33563700 \, x^{3} + 24606540 \, x^{2} - 7974123 \, x - 6363424}{130438 \, {\left (150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right )}} + \frac {376875}{14641} \, \log \left (5 \, x + 3\right ) - \frac {8829}{343} \, \log \left (3 \, x + 2\right ) - \frac {2736}{5021863} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 123 vs.
\(2 (61) = 122\).
time = 0.41, size = 123, normalized size = 1.64 \begin {gather*} \frac {2584404900 \, x^{3} + 1894703580 \, x^{2} + 258536250 \, {\left (150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right )} \log \left (5 \, x + 3\right ) - 258530778 \, {\left (150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right )} \log \left (3 \, x + 2\right ) - 5472 \, {\left (150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right )} \log \left (2 \, x - 1\right ) - 614007471 \, x - 489983648}{10043726 \, {\left (150 \, x^{4} + 205 \, x^{3} + 34 \, x^{2} - 51 \, x - 18\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 65, normalized size = 0.87 \begin {gather*} \frac {33563700 x^{3} + 24606540 x^{2} - 7974123 x - 6363424}{19565700 x^{4} + 26739790 x^{3} + 4434892 x^{2} - 6652338 x - 2347884} - \frac {2736 \log {\left (x - \frac {1}{2} \right )}}{5021863} + \frac {376875 \log {\left (x + \frac {3}{5} \right )}}{14641} - \frac {8829 \log {\left (x + \frac {2}{3} \right )}}{343} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.55, size = 86, normalized size = 1.15 \begin {gather*} \frac {81}{49 \, {\left (3 \, x + 2\right )}} + \frac {27 \, {\left (\frac {139939165}{3 \, x + 2} - \frac {31679854}{{\left (3 \, x + 2\right )}^{2}} - 37396350\right )}}{913066 \, {\left (\frac {7}{3 \, x + 2} - 2\right )} {\left (\frac {1}{3 \, x + 2} - 5\right )}^{2}} + \frac {376875}{14641} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {2736}{5021863} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 56, normalized size = 0.75 \begin {gather*} \frac {376875\,\ln \left (x+\frac {3}{5}\right )}{14641}-\frac {8829\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {2736\,\ln \left (x-\frac {1}{2}\right )}{5021863}-\frac {-\frac {111879\,x^3}{65219}-\frac {58587\,x^2}{46585}+\frac {2658041\,x}{6521900}+\frac {1590856}{4891425}}{x^4+\frac {41\,x^3}{30}+\frac {17\,x^2}{75}-\frac {17\,x}{50}-\frac {3}{25}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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