Optimal. Leaf size=8 \[ \frac{1}{2 \cos ^{-1}(x)^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0402161, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{1}{2 \cos ^{-1}(x)^2} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[1 - x^2]*ArcCos[x]^3),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.95948, size = 7, normalized size = 0.88 \[ \frac{1}{2 \operatorname{acos}^{2}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/acos(x)**3/(-x**2+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.003715, size = 8, normalized size = 1. \[ \frac{1}{2 \cos ^{-1}(x)^2} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[1 - x^2]*ArcCos[x]^3),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 7, normalized size = 0.9 \[{\frac{1}{2\, \left ( \arccos \left ( x \right ) \right ) ^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/arccos(x)^3/(-x^2+1)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.51361, size = 8, normalized size = 1. \[ \frac{1}{2 \, \arccos \left (x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^2 + 1)*arccos(x)^3),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.219914, size = 8, normalized size = 1. \[ \frac{1}{2 \, \arccos \left (x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^2 + 1)*arccos(x)^3),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.59682, size = 7, normalized size = 0.88 \[ \frac{1}{2 \operatorname{acos}^{2}{\left (x \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/acos(x)**3/(-x**2+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.204488, size = 8, normalized size = 1. \[ \frac{1}{2 \, \arccos \left (x\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^2 + 1)*arccos(x)^3),x, algorithm="giac")
[Out]