Optimal. Leaf size=32 \[ \frac{1}{11 (1-2 x)}-\frac{5}{121} \log (1-2 x)+\frac{5}{121} \log (5 x+3) \]
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Rubi [A] time = 0.0123018, 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} \[ \frac{1}{11 (1-2 x)}-\frac{5}{121} \log (1-2 x)+\frac{5}{121} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 44
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac{2}{11 (-1+2 x)^2}-\frac{10}{121 (-1+2 x)}+\frac{25}{121 (3+5 x)}\right ) \, dx\\ &=\frac{1}{11 (1-2 x)}-\frac{5}{121} \log (1-2 x)+\frac{5}{121} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0089032, size = 38, normalized size = 1.19 \[ \frac{(5-10 x) \log (1-2 x)+5 (2 x-1) \log (10 x+6)-11}{121 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 27, normalized size = 0.8 \begin{align*} -{\frac{1}{22\,x-11}}-{\frac{5\,\ln \left ( 2\,x-1 \right ) }{121}}+{\frac{5\,\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 = 1.11908, size = 35, normalized size = 1.09 \begin{align*} -\frac{1}{11 \,{\left (2 \, x - 1\right )}} + \frac{5}{121} \, \log \left (5 \, x + 3\right ) - \frac{5}{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 = 1.2648, size = 103, normalized size = 3.22 \begin{align*} \frac{5 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) - 5 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 11}{121 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.11428, size = 26, normalized size = 0.81 \begin{align*} - \frac{5 \log{\left (x - \frac{1}{2} \right )}}{121} + \frac{5 \log{\left (x + \frac{3}{5} \right )}}{121} - \frac{1}{22 x - 11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.21576, size = 34, normalized size = 1.06 \begin{align*} -\frac{1}{11 \,{\left (2 \, x - 1\right )}} + \frac{5}{121} \, \log \left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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