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 = 0.0202411, antiderivative size = 42, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0208269, size = 38, normalized size = 0.9 \[ \frac{1}{847} \left (-\frac{385}{5 x+3}-4 \log (1-2 x)+1089 \log (6 x+4)-1085 \log (10 x+6)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 35, normalized size = 0.8 \begin{align*} -{\frac{4\,\ln \left ( 2\,x-1 \right ) }{847}}+{\frac{9\,\ln \left ( 2+3\,x \right ) }{7}}-{\frac{5}{33+55\,x}}-{\frac{155\,\ln \left ( 3+5\,x \right ) }{121}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08209, size = 46, normalized size = 1.1 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57755, size = 150, normalized size = 3.57 \begin{align*} -\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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.162598, size = 36, normalized size = 0.86 \begin{align*} - \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.45049, size = 54, normalized size = 1.29 \begin{align*} -\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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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