Optimal. Leaf size=17 \[ \frac{1}{2} x \sin (\log (x))-\frac{1}{2} x \cos (\log (x)) \]
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Rubi [A] time = 0.0031254, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {4475} \[ \frac{1}{2} x \sin (\log (x))-\frac{1}{2} x \cos (\log (x)) \]
Antiderivative was successfully verified.
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Rule 4475
Rubi steps
\begin{align*} \int \sin (\log (x)) \, dx &=-\frac{1}{2} x \cos (\log (x))+\frac{1}{2} x \sin (\log (x))\\ \end{align*}
Mathematica [A] time = 0.0027508, size = 17, normalized size = 1. \[ \frac{1}{2} x \sin (\log (x))-\frac{1}{2} x \cos (\log (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 0.8 \begin{align*} -{\frac{x\cos \left ( \ln \left ( x \right ) \right ) }{2}}+{\frac{x\sin \left ( \ln \left ( x \right ) \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.93794, size = 16, normalized size = 0.94 \begin{align*} -\frac{1}{2} \, x{\left (\cos \left (\log \left (x\right )\right ) - \sin \left (\log \left (x\right )\right )\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.75441, size = 54, normalized size = 3.18 \begin{align*} -\frac{1}{2} \, x \cos \left (\log \left (x\right )\right ) + \frac{1}{2} \, x \sin \left (\log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.414042, size = 15, normalized size = 0.88 \begin{align*} \frac{x \sin{\left (\log{\left (x \right )} \right )}}{2} - \frac{x \cos{\left (\log{\left (x \right )} \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07497, size = 18, normalized size = 1.06 \begin{align*} -\frac{1}{2} \, x \cos \left (\log \left (x\right )\right ) + \frac{1}{2} \, x \sin \left (\log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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