Optimal. Leaf size=17 \[ \frac {\log (x)}{2}-\frac {1}{2} \log (3 x+2) \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, 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 29
Rule 31
Rule 36
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*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {\log (x)}{2}-\frac {1}{2} \log (3 x+2) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 13, normalized size = 0.76 \[ -\frac {1}{2} \, \log \left (3 \, x + 2\right ) + \frac {1}{2} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.15, size = 15, normalized size = 0.88 \[ -\frac {1}{2} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {1}{2} \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 14, normalized size = 0.82 \[ \frac {\ln \relax (x )}{2}-\frac {\ln \left (3 x +2\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 13, normalized size = 0.76 \[ -\frac {1}{2} \, \log \left (3 \, x + 2\right ) + \frac {1}{2} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.17, size = 10, normalized size = 0.59 \[ -\frac {\ln \left (\frac {2}{x}+3\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 12, normalized size = 0.71 \[ \frac {\log {\relax (x )}}{2} - \frac {\log {\left (x + \frac {2}{3} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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