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 = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, 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 = {4476} \[ \frac {1}{2} x \sin (\log (x))+\frac {1}{2} x \cos (\log (x)) \]
Antiderivative was successfully verified.
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Rule 4476
Rubi steps
\begin {align*} \int \cos (\log (x)) \, dx &=\frac {1}{2} x \cos (\log (x))+\frac {1}{2} x \sin (\log (x))\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ \frac {1}{2} x \sin (\log (x))+\frac {1}{2} x \cos (\log (x)) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \cos (\log (x)) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.93, size = 13, normalized size = 0.76 \[ \frac {1}{2} \, x \cos \left (\log \relax (x)\right ) + \frac {1}{2} \, x \sin \left (\log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.91, size = 13, normalized size = 0.76 \[ \frac {1}{2} \, x \cos \left (\log \relax (x)\right ) + \frac {1}{2} \, x \sin \left (\log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 0.82
method | result | size |
lookup | \(\frac {x \cos \left (\ln \relax (x )\right )}{2}+\frac {x \sin \left (\ln \relax (x )\right )}{2}\) | \(14\) |
default | \(\frac {x \cos \left (\ln \relax (x )\right )}{2}+\frac {x \sin \left (\ln \relax (x )\right )}{2}\) | \(14\) |
risch | \(\left (\frac {1}{4}-\frac {i}{4}\right ) x \,x^{i}+\left (\frac {1}{4}+\frac {i}{4}\right ) x \,x^{-i}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 10, normalized size = 0.59 \[ \frac {1}{2} \, x {\left (\cos \left (\log \relax (x)\right ) + \sin \left (\log \relax (x)\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 13, normalized size = 0.76 \[ \frac {\sqrt {2}\,x\,\sin \left (\frac {\pi }{4}+\ln \relax (x)\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 15, normalized size = 0.88 \[ \frac {x \sin {\left (\log {\relax (x )} \right )}}{2} + \frac {x \cos {\left (\log {\relax (x )} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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