Optimal. Leaf size=53 \[ \frac{111}{49 (3 x+2)}+\frac{3}{14 (3 x+2)^2}-\frac{8 \log (1-2 x)}{3773}-\frac{3897}{343} \log (3 x+2)+\frac{125}{11} \log (5 x+3) \]
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Rubi [A] time = 0.022631, 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 = {72} \[ \frac{111}{49 (3 x+2)}+\frac{3}{14 (3 x+2)^2}-\frac{8 \log (1-2 x)}{3773}-\frac{3897}{343} \log (3 x+2)+\frac{125}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x) (2+3 x)^3 (3+5 x)} \, dx &=\int \left (-\frac{16}{3773 (-1+2 x)}-\frac{9}{7 (2+3 x)^3}-\frac{333}{49 (2+3 x)^2}-\frac{11691}{343 (2+3 x)}+\frac{625}{11 (3+5 x)}\right ) \, dx\\ &=\frac{3}{14 (2+3 x)^2}+\frac{111}{49 (2+3 x)}-\frac{8 \log (1-2 x)}{3773}-\frac{3897}{343} \log (2+3 x)+\frac{125}{11} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0206484, size = 49, normalized size = 0.92 \[ \frac{\frac{8547}{3 x+2}+\frac{1617}{2 (3 x+2)^2}-8 \log (1-2 x)-42867 \log (6 x+4)+42875 \log (10 x+6)}{3773} \]
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 ) }{3773}}+{\frac{3}{14\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{111}{98+147\,x}}-{\frac{3897\,\ln \left ( 2+3\,x \right ) }{343}}+{\frac{125\,\ln \left ( 3+5\,x \right ) }{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04625, size = 59, normalized size = 1.11 \begin{align*} \frac{3 \,{\left (222 \, x + 155\right )}}{98 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{125}{11} \, \log \left (5 \, x + 3\right ) - \frac{3897}{343} \, \log \left (3 \, x + 2\right ) - \frac{8}{3773} \, \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 = 1.43646, size = 219, normalized size = 4.13 \begin{align*} \frac{85750 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (5 \, x + 3\right ) - 85734 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 16 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (2 \, x - 1\right ) + 51282 \, x + 35805}{7546 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.181788, size = 44, normalized size = 0.83 \begin{align*} \frac{666 x + 465}{882 x^{2} + 1176 x + 392} - \frac{8 \log{\left (x - \frac{1}{2} \right )}}{3773} + \frac{125 \log{\left (x + \frac{3}{5} \right )}}{11} - \frac{3897 \log{\left (x + \frac{2}{3} \right )}}{343} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.09301, size = 57, normalized size = 1.08 \begin{align*} \frac{3 \,{\left (222 \, x + 155\right )}}{98 \,{\left (3 \, x + 2\right )}^{2}} + \frac{125}{11} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{3897}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{8}{3773} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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