Optimal. Leaf size=10 \[ \frac{1}{2} \log ^2(e x) \]
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Rubi [A] time = 0.0061649, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {2301} \[ \frac{1}{2} \log ^2(e x) \]
Antiderivative was successfully verified.
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Rule 2301
Rubi steps
\begin{align*} \int \frac{\log (e x)}{x} \, dx &=\frac{1}{2} \log ^2(e x)\\ \end{align*}
Mathematica [A] time = 0.0009162, size = 10, normalized size = 1. \[ \frac{1}{2} \log ^2(e x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.058, size = 9, normalized size = 0.9 \begin{align*}{\frac{ \left ( \ln \left ( ex \right ) \right ) ^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.19513, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{2} \, \log \left (e x\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.81106, size = 22, normalized size = 2.2 \begin{align*} \frac{1}{2} \, \log \left (e x\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.086911, size = 7, normalized size = 0.7 \begin{align*} \frac{\log{\left (e x \right )}^{2}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.21108, size = 12, normalized size = 1.2 \begin{align*} \frac{1}{2} \, \log \left (x e\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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