Optimal. Leaf size=14 \[ x \log \left (\sqrt{x}\right )-\frac{x}{2} \]
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Rubi [A] time = 0.0011754, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {2295} \[ x \log \left (\sqrt{x}\right )-\frac{x}{2} \]
Antiderivative was successfully verified.
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Rule 2295
Rubi steps
\begin{align*} \int \log \left (\sqrt{x}\right ) \, dx &=-\frac{x}{2}+x \log \left (\sqrt{x}\right )\\ \end{align*}
Mathematica [A] time = 0.0005846, size = 12, normalized size = 0.86 \[ \frac{1}{2} (x \log (x)-x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 10, normalized size = 0.7 \begin{align*} -{\frac{x}{2}}+{\frac{x\ln \left ( x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.937011, size = 12, normalized size = 0.86 \begin{align*} \frac{1}{2} \, x \log \left (x\right ) - \frac{1}{2} \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.215, size = 30, normalized size = 2.14 \begin{align*} \frac{1}{2} \, x \log \left (x\right ) - \frac{1}{2} \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.079031, size = 8, normalized size = 0.57 \begin{align*} \frac{x \log{\left (x \right )}}{2} - \frac{x}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0501, size = 12, normalized size = 0.86 \begin{align*} \frac{1}{2} \, x \log \left (x\right ) - \frac{1}{2} \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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