Optimal. Leaf size=4 \[ -\cot (x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00735385, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5 \[ -\cot (x) \]
Antiderivative was successfully verified.
[In] Int[Csc[x]^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 0.473958, size = 7, normalized size = 1.75 \[ - \frac{\cos{\left (x \right )}}{\sin{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(csc(x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00273265, size = 4, normalized size = 1. \[ -\cot (x) \]
Antiderivative was successfully verified.
[In] Integrate[Csc[x]^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 5, normalized size = 1.3 \[ -\cot \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(csc(x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.42099, size = 8, normalized size = 2. \[ -\frac{1}{\tan \left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(csc(x)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.206007, size = 11, normalized size = 2.75 \[ -\frac{\cos \left (x\right )}{\sin \left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(csc(x)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.043857, size = 7, normalized size = 1.75 \[ - \frac{\cos{\left (x \right )}}{\sin{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(csc(x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.210021, size = 8, normalized size = 2. \[ -\frac{1}{\tan \left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(csc(x)^2,x, algorithm="giac")
[Out]