Optimal. Leaf size=43 \[ \frac{11}{49 (1-2 x)}+\frac{1}{49 (3 x+2)}-\frac{31}{343} \log (1-2 x)+\frac{31}{343} \log (3 x+2) \]
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Rubi [A] time = 0.0187948, 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} \[ \frac{11}{49 (1-2 x)}+\frac{1}{49 (3 x+2)}-\frac{31}{343} \log (1-2 x)+\frac{31}{343} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x)^2 (2+3 x)^2} \, dx &=\int \left (\frac{22}{49 (-1+2 x)^2}-\frac{62}{343 (-1+2 x)}-\frac{3}{49 (2+3 x)^2}+\frac{93}{343 (2+3 x)}\right ) \, dx\\ &=\frac{11}{49 (1-2 x)}+\frac{1}{49 (2+3 x)}-\frac{31}{343} \log (1-2 x)+\frac{31}{343} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0172281, size = 40, normalized size = 0.93 \[ \frac{-31 x-23}{49 \left (6 x^2+x-2\right )}-\frac{31}{343} \log (1-2 x)+\frac{31}{343} \log (3 x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 36, normalized size = 0.8 \begin{align*} -{\frac{11}{98\,x-49}}-{\frac{31\,\ln \left ( 2\,x-1 \right ) }{343}}+{\frac{1}{98+147\,x}}+{\frac{31\,\ln \left ( 2+3\,x \right ) }{343}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09234, size = 46, normalized size = 1.07 \begin{align*} -\frac{31 \, x + 23}{49 \,{\left (6 \, x^{2} + x - 2\right )}} + \frac{31}{343} \, \log \left (3 \, x + 2\right ) - \frac{31}{343} \, \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 = 1.33472, size = 142, normalized size = 3.3 \begin{align*} \frac{31 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (3 \, x + 2\right ) - 31 \,{\left (6 \, x^{2} + x - 2\right )} \log \left (2 \, x - 1\right ) - 217 \, x - 161}{343 \,{\left (6 \, x^{2} + x - 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.124881, size = 34, normalized size = 0.79 \begin{align*} - \frac{31 x + 23}{294 x^{2} + 49 x - 98} - \frac{31 \log{\left (x - \frac{1}{2} \right )}}{343} + \frac{31 \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 = 2.06592, size = 54, normalized size = 1.26 \begin{align*} \frac{1}{49 \,{\left (3 \, x + 2\right )}} + \frac{66}{343 \,{\left (\frac{7}{3 \, x + 2} - 2\right )}} - \frac{31}{343} \, \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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