Optimal. Leaf size=42 \[ \frac {3}{7 (3 x+2)}-\frac {4}{539} \log (1-2 x)-\frac {111}{49} \log (3 x+2)+\frac {25}{11} \log (5 x+3) \]
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Rubi [A] time = 0.02, antiderivative size = 42, 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 = {72} \[ \frac {3}{7 (3 x+2)}-\frac {4}{539} \log (1-2 x)-\frac {111}{49} \log (3 x+2)+\frac {25}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^2 (3+5 x)} \, dx &=\int \left (-\frac {8}{539 (-1+2 x)}-\frac {9}{7 (2+3 x)^2}-\frac {333}{49 (2+3 x)}+\frac {125}{11 (3+5 x)}\right ) \, dx\\ &=\frac {3}{7 (2+3 x)}-\frac {4}{539} \log (1-2 x)-\frac {111}{49} \log (2+3 x)+\frac {25}{11} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 38, normalized size = 0.90 \[ \frac {1}{539} \left (\frac {231}{3 x+2}-4 \log (1-2 x)-1221 \log (6 x+4)+1225 \log (10 x+6)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 50, normalized size = 1.19 \[ \frac {1225 \, {\left (3 \, x + 2\right )} \log \left (5 \, x + 3\right ) - 1221 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 4 \, {\left (3 \, x + 2\right )} \log \left (2 \, x - 1\right ) + 231}{539 \, {\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 40, normalized size = 0.95 \[ \frac {3}{7 \, {\left (3 \, x + 2\right )}} + \frac {25}{11} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {4}{539} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 35, normalized size = 0.83 \[ -\frac {4 \ln \left (2 x -1\right )}{539}-\frac {111 \ln \left (3 x +2\right )}{49}+\frac {25 \ln \left (5 x +3\right )}{11}+\frac {3}{7 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 34, normalized size = 0.81 \[ \frac {3}{7 \, {\left (3 \, x + 2\right )}} + \frac {25}{11} \, \log \left (5 \, x + 3\right ) - \frac {111}{49} \, \log \left (3 \, x + 2\right ) - \frac {4}{539} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.14, size = 26, normalized size = 0.62 \[ \frac {25\,\ln \left (x+\frac {3}{5}\right )}{11}-\frac {111\,\ln \left (x+\frac {2}{3}\right )}{49}-\frac {4\,\ln \left (x-\frac {1}{2}\right )}{539}+\frac {1}{7\,\left (x+\frac {2}{3}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 36, normalized size = 0.86 \[ - \frac {4 \log {\left (x - \frac {1}{2} \right )}}{539} + \frac {25 \log {\left (x + \frac {3}{5} \right )}}{11} - \frac {111 \log {\left (x + \frac {2}{3} \right )}}{49} + \frac {3}{21 x + 14} \]
Verification of antiderivative is not currently implemented for this CAS.
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