Optimal. Leaf size=17 \[ \frac{\log (x)}{2}-\frac{1}{2} \log (3 x+2) \]
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Rubi [A] time = 0.002297, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273, Rules used = {36, 29, 31} \[ \frac{\log (x)}{2}-\frac{1}{2} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 36
Rule 29
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{x (2+3 x)} \, dx &=\frac{1}{2} \int \frac{1}{x} \, dx-\frac{3}{2} \int \frac{1}{2+3 x} \, dx\\ &=\frac{\log (x)}{2}-\frac{1}{2} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0053061, size = 17, normalized size = 1. \[ \frac{\log (x)}{2}-\frac{1}{2} \log (3 x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 14, normalized size = 0.8 \begin{align*}{\frac{\ln \left ( x \right ) }{2}}-{\frac{\ln \left ( 2+3\,x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03794, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{2} \, \log \left (3 \, x + 2\right ) + \frac{1}{2} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72443, size = 43, normalized size = 2.53 \begin{align*} -\frac{1}{2} \, \log \left (3 \, x + 2\right ) + \frac{1}{2} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.12257, size = 12, normalized size = 0.71 \begin{align*} \frac{\log{\left (x \right )}}{2} - \frac{\log{\left (x + \frac{2}{3} \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.22379, size = 20, normalized size = 1.18 \begin{align*} -\frac{1}{2} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac{1}{2} \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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