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 = 0.017436, 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} \[ \frac{3}{7 (3 x+2)}-\frac{4}{539} \log (1-2 x)-\frac{111}{49} \log (3 x+2)+\frac{25}{11} \log (5 x+3) \]
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*}
Mathematica [A] time = 0.0199891, size = 38, normalized size = 0.9 \[ \frac{1}{539} \left (\frac{231}{3 x+2}-4 \log (1-2 x)-1221 \log (6 x+4)+1225 \log (10 x+6)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 35, normalized size = 0.8 \begin{align*} -{\frac{4\,\ln \left ( 2\,x-1 \right ) }{539}}+{\frac{3}{14+21\,x}}-{\frac{111\,\ln \left ( 2+3\,x \right ) }{49}}+{\frac{25\,\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 = 1.16987, size = 46, normalized size = 1.1 \begin{align*} \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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.40554, size = 149, normalized size = 3.55 \begin{align*} \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 )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.159433, size = 36, normalized size = 0.86 \begin{align*} - \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.45932, size = 54, normalized size = 1.29 \begin{align*} \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 ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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