Optimal. Leaf size=7 \[ -\cos (x \log (x)) \]
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Rubi [A] time = 0.0269251, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {4511} \[ -\cos (x \log (x)) \]
Antiderivative was successfully verified.
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Rule 4511
Rubi steps
\begin{align*} \int (\sin (x \log (x))+\log (x) \sin (x \log (x))) \, dx &=\int \sin (x \log (x)) \, dx+\int \log (x) \sin (x \log (x)) \, dx\\ &=-\cos (x \log (x))\\ \end{align*}
Mathematica [A] time = 0.108954, size = 7, normalized size = 1. \[ -\cos (x \log (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.017, size = 8, normalized size = 1.1 \begin{align*} -\cos \left ( x\ln \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.2649, size = 9, normalized size = 1.29 \begin{align*} -\cos \left (x \log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.19406, size = 22, normalized size = 3.14 \begin{align*} -\cos \left (x \log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (\log{\left (x \right )} + 1\right ) \sin{\left (x \log{\left (x \right )} \right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \log \left (x\right ) \sin \left (x \log \left (x\right )\right ) + \sin \left (x \log \left (x\right )\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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