Optimal. Leaf size=12 \[ x \log \left (\frac{x}{2}\right )-x \]
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Rubi [A] time = 0.0013106, antiderivative size = 12, 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} \[ x \log \left (\frac{x}{2}\right )-x \]
Antiderivative was successfully verified.
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Rule 2295
Rubi steps
\begin{align*} \int \log \left (\frac{x}{2}\right ) \, dx &=-x+x \log \left (\frac{x}{2}\right )\\ \end{align*}
Mathematica [A] time = 0.0006773, size = 12, normalized size = 1. \[ x \log \left (\frac{x}{2}\right )-x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 0.9 \begin{align*} -x+x\ln \left ({\frac{x}{2}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.937229, size = 14, normalized size = 1.17 \begin{align*} x \log \left (\frac{1}{2} \, x\right ) - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.3514, size = 24, normalized size = 2. \begin{align*} x \log \left (\frac{1}{2} \, x\right ) - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.081452, size = 7, normalized size = 0.58 \begin{align*} x \log{\left (\frac{x}{2} \right )} - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04918, size = 14, normalized size = 1.17 \begin{align*} x \log \left (\frac{1}{2} \, x\right ) - x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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