Optimal. Leaf size=16 \[ \sin ^{-1}(x)-\sqrt{1-x^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0266875, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \sin ^{-1}(x)-\sqrt{1-x^2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - x^2]/(1 - x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.65262, size = 10, normalized size = 0.62 \[ - \sqrt{- x^{2} + 1} + \operatorname{asin}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x**2+1)**(1/2)/(1-x),x)
[Out]
_______________________________________________________________________________________
Mathematica [B] time = 0.046004, size = 54, normalized size = 3.38 \[ \sqrt{1-x^2} \left (\frac{2 \log \left (\sqrt{-x-1}+\sqrt{1-x}\right )}{\sqrt{-x-1} \sqrt{1-x}}-1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - x^2]/(1 - x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.006, size = 20, normalized size = 1.3 \[ -\sqrt{- \left ( -1+x \right ) ^{2}-2\,x+2}+\arcsin \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^2+1)^(1/2)/(1-x),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.783426, size = 19, normalized size = 1.19 \[ -\sqrt{-x^{2} + 1} + \arcsin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(-x^2 + 1)/(x - 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.216297, size = 63, normalized size = 3.94 \[ \frac{x^{2} - 2 \,{\left (\sqrt{-x^{2} + 1} - 1\right )} \arctan \left (\frac{\sqrt{-x^{2} + 1} - 1}{x}\right )}{\sqrt{-x^{2} + 1} - 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(-x^2 + 1)/(x - 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 5.7653, size = 17, normalized size = 1.06 \[ - \begin{cases} \sqrt{- x^{2} + 1} - \operatorname{asin}{\left (x \right )} & \text{for}\: x > -1 \wedge x < 1 \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**2+1)**(1/2)/(1-x),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.212457, size = 19, normalized size = 1.19 \[ -\sqrt{-x^{2} + 1} + \arcsin \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-sqrt(-x^2 + 1)/(x - 1),x, algorithm="giac")
[Out]