Optimal. Leaf size=4 \[ \log (\log (\sin (x))) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0304205, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375 \[ \log (\log (\sin (x))) \]
Antiderivative was successfully verified.
[In] Int[Cot[x]/Log[Sin[x]],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.18413, size = 5, normalized size = 1.25 \[ \log{\left (\log{\left (\sin{\left (x \right )} \right )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(cot(x)/ln(sin(x)),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0042337, size = 4, normalized size = 1. \[ \log (\log (\sin (x))) \]
Antiderivative was successfully verified.
[In] Integrate[Cot[x]/Log[Sin[x]],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.012, size = 5, normalized size = 1.3 \[ \ln \left ( \ln \left ( \sin \left ( x \right ) \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(cot(x)/ln(sin(x)),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44547, size = 5, normalized size = 1.25 \[ \log \left (\log \left (\sin \left (x\right )\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x)/log(sin(x)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.215226, size = 5, normalized size = 1.25 \[ \log \left (\log \left (\sin \left (x\right )\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x)/log(sin(x)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\cot{\left (x \right )}}{\log{\left (\sin{\left (x \right )} \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x)/ln(sin(x)),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.221748, size = 7, normalized size = 1.75 \[{\rm ln}\left ({\left |{\rm ln}\left (\sin \left (x\right )\right ) \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(cot(x)/log(sin(x)),x, algorithm="giac")
[Out]