Optimal. Leaf size=32 \[ \frac{11}{14 (1-2 x)}+\frac{1}{49} \log (1-2 x)-\frac{1}{49} \log (3 x+2) \]
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Rubi [A] time = 0.014893, antiderivative size = 32, 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} \[ \frac{11}{14 (1-2 x)}+\frac{1}{49} \log (1-2 x)-\frac{1}{49} \log (3 x+2) \]
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)} \, dx &=\int \left (\frac{11}{7 (-1+2 x)^2}+\frac{2}{49 (-1+2 x)}-\frac{3}{49 (2+3 x)}\right ) \, dx\\ &=\frac{11}{14 (1-2 x)}+\frac{1}{49} \log (1-2 x)-\frac{1}{49} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0126618, size = 37, normalized size = 1.16 \[ \frac{(4 x-2) \log (1-2 x)+(2-4 x) \log (6 x+4)-77}{98 (2 x-1)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 27, normalized size = 0.8 \begin{align*} -{\frac{11}{28\,x-14}}+{\frac{\ln \left ( 2\,x-1 \right ) }{49}}-{\frac{\ln \left ( 2+3\,x \right ) }{49}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08185, size = 35, normalized size = 1.09 \begin{align*} -\frac{11}{14 \,{\left (2 \, x - 1\right )}} - \frac{1}{49} \, \log \left (3 \, x + 2\right ) + \frac{1}{49} \, \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 = 1.37141, size = 103, normalized size = 3.22 \begin{align*} -\frac{2 \,{\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) - 2 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) + 77}{98 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.109262, size = 22, normalized size = 0.69 \begin{align*} \frac{\log{\left (x - \frac{1}{2} \right )}}{49} - \frac{\log{\left (x + \frac{2}{3} \right )}}{49} - \frac{11}{28 x - 14} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.35081, size = 34, normalized size = 1.06 \begin{align*} -\frac{11}{14 \,{\left (2 \, x - 1\right )}} - \frac{1}{49} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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