Optimal. Leaf size=3 \[ \log (\sin (x)) \]
[Out]
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Rubi [A] time = 0.00330414, antiderivative size = 3, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ \log (\sin (x)) \]
Antiderivative was successfully verified.
[In] Int[Cot[x],x]
[Out]
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Rubi in Sympy [A] time = 0.031111, size = 3, normalized size = 1. \[ \log{\left (\sin{\left (x \right )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cot(x),x)
[Out]
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Mathematica [A] time = 0.00322735, size = 3, normalized size = 1. \[ \log (\sin (x)) \]
Antiderivative was successfully verified.
[In] Integrate[Cot[x],x]
[Out]
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Maple [A] time = 0., size = 4, normalized size = 1.3 \[ \ln \left ( \sin \left ( x \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cot(x),x)
[Out]
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Maxima [A] time = 1.44271, size = 4, normalized size = 1.33 \[ \log \left (\sin \left (x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221127, size = 15, normalized size = 5. \[ \frac{1}{2} \, \log \left (-\frac{1}{2} \, \cos \left (2 \, x\right ) + \frac{1}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.043343, size = 3, normalized size = 1. \[ \log{\left (\sin{\left (x \right )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x),x)
[Out]
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GIAC/XCAS [A] time = 0.201969, size = 15, normalized size = 5. \[ \frac{1}{2} \,{\rm ln}\left (-\cos \left (x\right )^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x),x, algorithm="giac")
[Out]