Optimal. Leaf size=64 \[ \frac {404}{41503 (1-2 x)}+\frac {27}{343 (3 x+2)}+\frac {2}{539 (1-2 x)^2}-\frac {27208 \log (1-2 x)}{3195731}-\frac {1107 \log (3 x+2)}{2401}+\frac {625 \log (5 x+3)}{1331} \]
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Rubi [A] time = 0.03, antiderivative size = 64, 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} \[ \frac {404}{41503 (1-2 x)}+\frac {27}{343 (3 x+2)}+\frac {2}{539 (1-2 x)^2}-\frac {27208 \log (1-2 x)}{3195731}-\frac {1107 \log (3 x+2)}{2401}+\frac {625 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)} \, dx &=\int \left (-\frac {8}{539 (-1+2 x)^3}+\frac {808}{41503 (-1+2 x)^2}-\frac {54416}{3195731 (-1+2 x)}-\frac {81}{343 (2+3 x)^2}-\frac {3321}{2401 (2+3 x)}+\frac {3125}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {2}{539 (1-2 x)^2}+\frac {404}{41503 (1-2 x)}+\frac {27}{343 (2+3 x)}-\frac {27208 \log (1-2 x)}{3195731}-\frac {1107 \log (2+3 x)}{2401}+\frac {625 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A] time = 0.08, size = 57, normalized size = 0.89 \[ \frac {\frac {77 \left (10644 x^2-13010 x+4383\right )}{(1-2 x)^2 (3 x+2)}-27208 \log (5-10 x)-1473417 \log (5 (3 x+2))+1500625 \log (5 x+3)}{3195731} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 98, normalized size = 1.53 \[ \frac {819588 \, x^{2} + 1500625 \, {\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )} \log \left (5 \, x + 3\right ) - 1473417 \, {\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 27208 \, {\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )} \log \left (2 \, x - 1\right ) - 1001770 \, x + 337491}{3195731 \, {\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.17, size = 66, normalized size = 1.03 \[ \frac {27}{343 \, {\left (3 \, x + 2\right )}} + \frac {24 \, {\left (\frac {938}{3 \, x + 2} - 235\right )}}{290521 \, {\left (\frac {7}{3 \, x + 2} - 2\right )}^{2}} + \frac {625}{1331} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {27208}{3195731} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 53, normalized size = 0.83 \[ -\frac {27208 \ln \left (2 x -1\right )}{3195731}-\frac {1107 \ln \left (3 x +2\right )}{2401}+\frac {625 \ln \left (5 x +3\right )}{1331}+\frac {27}{343 \left (3 x +2\right )}+\frac {2}{539 \left (2 x -1\right )^{2}}-\frac {404}{41503 \left (2 x -1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 54, normalized size = 0.84 \[ \frac {10644 \, x^{2} - 13010 \, x + 4383}{41503 \, {\left (12 \, x^{3} - 4 \, x^{2} - 5 \, x + 2\right )}} + \frac {625}{1331} \, \log \left (5 \, x + 3\right ) - \frac {1107}{2401} \, \log \left (3 \, x + 2\right ) - \frac {27208}{3195731} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 48, normalized size = 0.75 \[ \frac {625\,\ln \left (x+\frac {3}{5}\right )}{1331}-\frac {1107\,\ln \left (x+\frac {2}{3}\right )}{2401}-\frac {27208\,\ln \left (x-\frac {1}{2}\right )}{3195731}-\frac {\frac {887\,x^2}{41503}-\frac {6505\,x}{249018}+\frac {1461}{166012}}{-x^3+\frac {x^2}{3}+\frac {5\,x}{12}-\frac {1}{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 54, normalized size = 0.84 \[ - \frac {- 10644 x^{2} + 13010 x - 4383}{498036 x^{3} - 166012 x^{2} - 207515 x + 83006} - \frac {27208 \log {\left (x - \frac {1}{2} \right )}}{3195731} + \frac {625 \log {\left (x + \frac {3}{5} \right )}}{1331} - \frac {1107 \log {\left (x + \frac {2}{3} \right )}}{2401} \]
Verification of antiderivative is not currently implemented for this CAS.
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