Optimal. Leaf size=32 \[ \frac{1}{21 (3 x+2)}-\frac{11}{49} \log (1-2 x)+\frac{11}{49} \log (3 x+2) \]
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Rubi [A] time = 0.0152345, 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} \[ \frac{1}{21 (3 x+2)}-\frac{11}{49} \log (1-2 x)+\frac{11}{49} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{3+5 x}{(1-2 x) (2+3 x)^2} \, dx &=\int \left (-\frac{22}{49 (-1+2 x)}-\frac{1}{7 (2+3 x)^2}+\frac{33}{49 (2+3 x)}\right ) \, dx\\ &=\frac{1}{21 (2+3 x)}-\frac{11}{49} \log (1-2 x)+\frac{11}{49} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0144604, size = 30, normalized size = 0.94 \[ \frac{1}{147} \left (\frac{7}{3 x+2}-33 \log (3-6 x)+33 \log (3 x+2)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 27, normalized size = 0.8 \begin{align*} -{\frac{11\,\ln \left ( 2\,x-1 \right ) }{49}}+{\frac{1}{42+63\,x}}+{\frac{11\,\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 = 1.03227, size = 35, normalized size = 1.09 \begin{align*} \frac{1}{21 \,{\left (3 \, x + 2\right )}} + \frac{11}{49} \, \log \left (3 \, x + 2\right ) - \frac{11}{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 = 1.46824, size = 104, normalized size = 3.25 \begin{align*} \frac{33 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 33 \,{\left (3 \, x + 2\right )} \log \left (2 \, x - 1\right ) + 7}{147 \,{\left (3 \, x + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.117083, size = 26, normalized size = 0.81 \begin{align*} - \frac{11 \log{\left (x - \frac{1}{2} \right )}}{49} + \frac{11 \log{\left (x + \frac{2}{3} \right )}}{49} + \frac{1}{63 x + 42} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.09648, size = 34, normalized size = 1.06 \begin{align*} \frac{1}{21 \,{\left (3 \, x + 2\right )}} - \frac{11}{49} \, \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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