Optimal. Leaf size=32 \[ -\frac{1}{11 (5 x+3)}-\frac{2}{121} \log (1-2 x)+\frac{2}{121} \log (5 x+3) \]
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Rubi [A] time = 0.0111126, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {44} \[ -\frac{1}{11 (5 x+3)}-\frac{2}{121} \log (1-2 x)+\frac{2}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 44
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x) (3+5 x)^2} \, dx &=\int \left (-\frac{4}{121 (-1+2 x)}+\frac{5}{11 (3+5 x)^2}+\frac{10}{121 (3+5 x)}\right ) \, dx\\ &=-\frac{1}{11 (3+5 x)}-\frac{2}{121} \log (1-2 x)+\frac{2}{121} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0109573, size = 30, normalized size = 0.94 \[ \frac{1}{121} \left (-\frac{11}{5 x+3}-2 \log (5-10 x)+2 \log (5 x+3)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 27, normalized size = 0.8 \begin{align*} -{\frac{2\,\ln \left ( 2\,x-1 \right ) }{121}}-{\frac{1}{33+55\,x}}+{\frac{2\,\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 = 2.06305, size = 35, normalized size = 1.09 \begin{align*} -\frac{1}{11 \,{\left (5 \, x + 3\right )}} + \frac{2}{121} \, \log \left (5 \, x + 3\right ) - \frac{2}{121} \, \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 = 1.59599, size = 103, normalized size = 3.22 \begin{align*} \frac{2 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 2 \,{\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 11}{121 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.117526, size = 26, normalized size = 0.81 \begin{align*} - \frac{2 \log{\left (x - \frac{1}{2} \right )}}{121} + \frac{2 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{1}{55 x + 33} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.61284, size = 34, normalized size = 1.06 \begin{align*} -\frac{1}{11 \,{\left (5 \, x + 3\right )}} - \frac{2}{121} \, \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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