Optimal. Leaf size=42 \[ -\frac {5}{11 (5 x+3)}-\frac {4}{847} \log (1-2 x)+\frac {9}{7} \log (3 x+2)-\frac {155}{121} \log (5 x+3) \]
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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} \[ -\frac {5}{11 (5 x+3)}-\frac {4}{847} \log (1-2 x)+\frac {9}{7} \log (3 x+2)-\frac {155}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x) (3+5 x)^2} \, dx &=\int \left (-\frac {8}{847 (-1+2 x)}+\frac {27}{7 (2+3 x)}+\frac {25}{11 (3+5 x)^2}-\frac {775}{121 (3+5 x)}\right ) \, dx\\ &=-\frac {5}{11 (3+5 x)}-\frac {4}{847} \log (1-2 x)+\frac {9}{7} \log (2+3 x)-\frac {155}{121} \log (3+5 x)\\ \end {align*}
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Mathematica [A] time = 0.03, size = 38, normalized size = 0.90 \[ \frac {1}{847} \left (-\frac {385}{5 x+3}-4 \log (1-2 x)+1089 \log (6 x+4)-1085 \log (10 x+6)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 50, normalized size = 1.19 \[ -\frac {1085 \, {\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1089 \, {\left (5 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 4 \, {\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 385}{847 \, {\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 40, normalized size = 0.95 \[ -\frac {5}{11 \, {\left (5 \, x + 3\right )}} + \frac {9}{7} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {4}{847} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \]
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 \[ -\frac {4 \ln \left (2 x -1\right )}{847}+\frac {9 \ln \left (3 x +2\right )}{7}-\frac {155 \ln \left (5 x +3\right )}{121}-\frac {5}{11 \left (5 x +3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 34, normalized size = 0.81 \[ -\frac {5}{11 \, {\left (5 \, x + 3\right )}} - \frac {155}{121} \, \log \left (5 \, x + 3\right ) + \frac {9}{7} \, \log \left (3 \, x + 2\right ) - \frac {4}{847} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.11, size = 28, normalized size = 0.67 \[ \frac {9\,\ln \left (x+\frac {2}{3}\right )}{7}-\frac {4\,\ln \left (x-\frac {1}{2}\right )}{847}-\frac {155\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {1}{11\,\left (x+\frac {3}{5}\right )} \]
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 \[ - \frac {4 \log {\left (x - \frac {1}{2} \right )}}{847} - \frac {155 \log {\left (x + \frac {3}{5} \right )}}{121} + \frac {9 \log {\left (x + \frac {2}{3} \right )}}{7} - \frac {5}{55 x + 33} \]
Verification of antiderivative is not currently implemented for this CAS.
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