Optimal. Leaf size=17 \[ \frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x)) \]
[Out]
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Rubi [A] time = 0.00728153, 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 \[ \frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x)) \]
Antiderivative was successfully verified.
[In] Int[Cos[Log[x]],x]
[Out]
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Rubi in Sympy [A] time = 0.473577, size = 15, normalized size = 0.88 \[ \frac{x \sin{\left (\log{\left (x \right )} \right )}}{2} + \frac{x \cos{\left (\log{\left (x \right )} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cos(ln(x)),x)
[Out]
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Mathematica [A] time = 0.00439241, size = 17, normalized size = 1. \[ \frac{1}{2} x \sin (\log (x))+\frac{1}{2} x \cos (\log (x)) \]
Antiderivative was successfully verified.
[In] Integrate[Cos[Log[x]],x]
[Out]
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Maple [A] time = 0., size = 14, normalized size = 0.8 \[{\frac{x\cos \left ( \ln \left ( x \right ) \right ) }{2}}+{\frac{x\sin \left ( \ln \left ( x \right ) \right ) }{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cos(ln(x)),x)
[Out]
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Maxima [A] time = 1.40124, size = 14, normalized size = 0.82 \[ \frac{1}{2} \, x{\left (\cos \left (\log \left (x\right )\right ) + \sin \left (\log \left (x\right )\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(log(x)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.239583, size = 18, normalized size = 1.06 \[ \frac{1}{2} \, x \cos \left (\log \left (x\right )\right ) + \frac{1}{2} \, x \sin \left (\log \left (x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(log(x)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.521858, size = 15, normalized size = 0.88 \[ \frac{x \sin{\left (\log{\left (x \right )} \right )}}{2} + \frac{x \cos{\left (\log{\left (x \right )} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(ln(x)),x)
[Out]
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GIAC/XCAS [A] time = 0.215739, size = 18, normalized size = 1.06 \[ \frac{1}{2} \, x \cos \left ({\rm ln}\left (x\right )\right ) + \frac{1}{2} \, x \sin \left ({\rm ln}\left (x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cos(log(x)),x, algorithm="giac")
[Out]