Optimal. Leaf size=43 \[ \frac{7}{121 (1-2 x)}-\frac{1}{121 (5 x+3)}-\frac{37 \log (1-2 x)}{1331}+\frac{37 \log (5 x+3)}{1331} \]
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Rubi [A] time = 0.0171225, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ \frac{7}{121 (1-2 x)}-\frac{1}{121 (5 x+3)}-\frac{37 \log (1-2 x)}{1331}+\frac{37 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{2+3 x}{(1-2 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac{14}{121 (-1+2 x)^2}-\frac{74}{1331 (-1+2 x)}+\frac{5}{121 (3+5 x)^2}+\frac{185}{1331 (3+5 x)}\right ) \, dx\\ &=\frac{7}{121 (1-2 x)}-\frac{1}{121 (3+5 x)}-\frac{37 \log (1-2 x)}{1331}+\frac{37 \log (3+5 x)}{1331}\\ \end{align*}
Mathematica [A] time = 0.0150774, size = 40, normalized size = 0.93 \[ \frac{-37 x-20}{121 \left (10 x^2+x-3\right )}-\frac{37 \log (1-2 x)}{1331}+\frac{37 \log (5 x+3)}{1331} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 36, normalized size = 0.8 \begin{align*} -{\frac{7}{242\,x-121}}-{\frac{37\,\ln \left ( 2\,x-1 \right ) }{1331}}-{\frac{1}{363+605\,x}}+{\frac{37\,\ln \left ( 3+5\,x \right ) }{1331}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0772, size = 46, normalized size = 1.07 \begin{align*} -\frac{37 \, x + 20}{121 \,{\left (10 \, x^{2} + x - 3\right )}} + \frac{37}{1331} \, \log \left (5 \, x + 3\right ) - \frac{37}{1331} \, \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 = 1.31441, size = 147, normalized size = 3.42 \begin{align*} \frac{37 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (5 \, x + 3\right ) - 37 \,{\left (10 \, x^{2} + x - 3\right )} \log \left (2 \, x - 1\right ) - 407 \, x - 220}{1331 \,{\left (10 \, x^{2} + x - 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.132012, size = 34, normalized size = 0.79 \begin{align*} - \frac{37 x + 20}{1210 x^{2} + 121 x - 363} - \frac{37 \log{\left (x - \frac{1}{2} \right )}}{1331} + \frac{37 \log{\left (x + \frac{3}{5} \right )}}{1331} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.15209, size = 54, normalized size = 1.26 \begin{align*} -\frac{1}{121 \,{\left (5 \, x + 3\right )}} + \frac{70}{1331 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}} - \frac{37}{1331} \, \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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