Optimal. Leaf size=53 \[ -\frac{9}{7 (3 x+2)}-\frac{25}{11 (5 x+3)}-\frac{8 \log (1-2 x)}{5929}+\frac{648}{49} \log (3 x+2)-\frac{1600}{121} \log (5 x+3) \]
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Rubi [A] time = 0.0230057, antiderivative size = 53, 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 = {88} \[ -\frac{9}{7 (3 x+2)}-\frac{25}{11 (5 x+3)}-\frac{8 \log (1-2 x)}{5929}+\frac{648}{49} \log (3 x+2)-\frac{1600}{121} \log (5 x+3) \]
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)^2} \, dx &=\int \left (-\frac{16}{5929 (-1+2 x)}+\frac{27}{7 (2+3 x)^2}+\frac{1944}{49 (2+3 x)}+\frac{125}{11 (3+5 x)^2}-\frac{8000}{121 (3+5 x)}\right ) \, dx\\ &=-\frac{9}{7 (2+3 x)}-\frac{25}{11 (3+5 x)}-\frac{8 \log (1-2 x)}{5929}+\frac{648}{49} \log (2+3 x)-\frac{1600}{121} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0248485, size = 47, normalized size = 0.89 \[ \frac{2 \left (-\frac{7623}{6 x+4}-\frac{13475}{10 x+6}-4 \log (1-2 x)+39204 \log (6 x+4)-39200 \log (10 x+6)\right )}{5929} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 44, normalized size = 0.8 \begin{align*} -{\frac{8\,\ln \left ( 2\,x-1 \right ) }{5929}}-{\frac{9}{14+21\,x}}+{\frac{648\,\ln \left ( 2+3\,x \right ) }{49}}-{\frac{25}{33+55\,x}}-{\frac{1600\,\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 = 1.10766, size = 59, normalized size = 1.11 \begin{align*} -\frac{1020 \, x + 647}{77 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} - \frac{1600}{121} \, \log \left (5 \, x + 3\right ) + \frac{648}{49} \, \log \left (3 \, x + 2\right ) - \frac{8}{5929} \, \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 = 1.55902, size = 224, normalized size = 4.23 \begin{align*} -\frac{78400 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 78408 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 8 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (2 \, x - 1\right ) + 78540 \, x + 49819}{5929 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.180936, size = 44, normalized size = 0.83 \begin{align*} - \frac{1020 x + 647}{1155 x^{2} + 1463 x + 462} - \frac{8 \log{\left (x - \frac{1}{2} \right )}}{5929} - \frac{1600 \log{\left (x + \frac{3}{5} \right )}}{121} + \frac{648 \log{\left (x + \frac{2}{3} \right )}}{49} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.46677, size = 72, normalized size = 1.36 \begin{align*} -\frac{25}{11 \,{\left (5 \, x + 3\right )}} + \frac{135}{7 \,{\left (\frac{1}{5 \, x + 3} + 3\right )}} + \frac{648}{49} \, \log \left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) - \frac{8}{5929} \, \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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