Optimal. Leaf size=7 \[ -\cos (x \log (x)) \]
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Rubi [A] time = 0.03, antiderivative size = 7, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.11, size = 7, normalized size = 1.00 \[ -\cos (x \log (x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 7, normalized size = 1.00 \[ -\cos \left (x \log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 8, normalized size = 1.14 \[ -\cos \left (x \ln \relax (x )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.09, size = 7, normalized size = 1.00 \[ -\cos \left (x \log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.42, size = 7, normalized size = 1.00 \[ -\cos \left (x\,\ln \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (\log {\relax (x )} + 1\right ) \sin {\left (x \log {\relax (x )} \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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