Optimal. Leaf size=64 \[ \frac {27}{7 (3 x+2)}+\frac {1600}{121 (5 x+3)}-\frac {25}{22 (5 x+3)^2}-\frac {16 \log (1-2 x)}{65219}-\frac {2889}{49} \log (3 x+2)+\frac {78475 \log (5 x+3)}{1331} \]
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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} \[ \frac {27}{7 (3 x+2)}+\frac {1600}{121 (5 x+3)}-\frac {25}{22 (5 x+3)^2}-\frac {16 \log (1-2 x)}{65219}-\frac {2889}{49} \log (3 x+2)+\frac {78475 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)^3} \, dx &=\int \left (-\frac {32}{65219 (-1+2 x)}-\frac {81}{7 (2+3 x)^2}-\frac {8667}{49 (2+3 x)}+\frac {125}{11 (3+5 x)^3}-\frac {8000}{121 (3+5 x)^2}+\frac {392375}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {27}{7 (2+3 x)}-\frac {25}{22 (3+5 x)^2}+\frac {1600}{121 (3+5 x)}-\frac {16 \log (1-2 x)}{65219}-\frac {2889}{49} \log (2+3 x)+\frac {78475 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 60, normalized size = 0.94 \[ \frac {27}{21 x+14}+\frac {1600}{605 x+363}-\frac {25}{22 (5 x+3)^2}-\frac {16 \log (1-2 x)}{65219}-\frac {2889}{49} \log (6 x+4)+\frac {78475 \log (10 x+6)}{1331} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.04, size = 98, normalized size = 1.53 \[ \frac {38449950 \, x^{2} + 7690550 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 7690518 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (3 \, x + 2\right ) - 32 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (2 \, x - 1\right ) + 47420065 \, x + 14580412}{130438 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 64, normalized size = 1.00 \[ \frac {27}{7 \, {\left (3 \, x + 2\right )}} - \frac {375 \, {\left (\frac {194}{3 \, x + 2} - 805\right )}}{242 \, {\left (\frac {1}{3 \, x + 2} - 5\right )}^{2}} + \frac {78475}{1331} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {16}{65219} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \]
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 \[ -\frac {16 \ln \left (2 x -1\right )}{65219}-\frac {2889 \ln \left (3 x +2\right )}{49}+\frac {78475 \ln \left (5 x +3\right )}{1331}-\frac {25}{22 \left (5 x +3\right )^{2}}+\frac {1600}{121 \left (5 x +3\right )}+\frac {27}{7 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 54, normalized size = 0.84 \[ \frac {499350 \, x^{2} + 615845 \, x + 189356}{1694 \, {\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} + \frac {78475}{1331} \, \log \left (5 \, x + 3\right ) - \frac {2889}{49} \, \log \left (3 \, x + 2\right ) - \frac {16}{65219} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 45, normalized size = 0.70 \[ \frac {78475\,\ln \left (x+\frac {3}{5}\right )}{1331}-\frac {2889\,\ln \left (x+\frac {2}{3}\right )}{49}-\frac {16\,\ln \left (x-\frac {1}{2}\right )}{65219}+\frac {\frac {3329\,x^2}{847}+\frac {123169\,x}{25410}+\frac {94678}{63525}}{x^3+\frac {28\,x^2}{15}+\frac {29\,x}{25}+\frac {6}{25}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 56, normalized size = 0.88 \[ - \frac {- 499350 x^{2} - 615845 x - 189356}{127050 x^{3} + 237160 x^{2} + 147378 x + 30492} - \frac {16 \log {\left (x - \frac {1}{2} \right )}}{65219} + \frac {78475 \log {\left (x + \frac {3}{5} \right )}}{1331} - \frac {2889 \log {\left (x + \frac {2}{3} \right )}}{49} \]
Verification of antiderivative is not currently implemented for this CAS.
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