Optimal. Leaf size=63 \[ \frac{1}{4} \sqrt{-x^2+\sqrt{x^2-1} x+1} \left (\sqrt{x^2-1}+3 x\right )+\frac{3 \sin ^{-1}\left (x-\sqrt{x^2-1}\right )}{4 \sqrt{2}} \]
[Out]
_______________________________________________________________________________________
Rubi [F] time = 0.0462596, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\sqrt{1-x^2+x \sqrt{-1+x^2}},x\right ) \]
Verification is Not applicable to the result.
[In] Int[Sqrt[1 - x^2 + x*Sqrt[-1 + x^2]],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{- x^{2} + x \sqrt{x^{2} - 1} + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-x**2+x*(x**2-1)**(1/2))**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0277576, size = 0, normalized size = 0. \[ \int \sqrt{1-x^2+x \sqrt{-1+x^2}} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[Sqrt[1 - x^2 + x*Sqrt[-1 + x^2]],x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.011, size = 0, normalized size = 0. \[ \int \sqrt{1-{x}^{2}+x\sqrt{{x}^{2}-1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-x^2+x*(x^2-1)^(1/2))^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{-x^{2} + \sqrt{x^{2} - 1} x + 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + sqrt(x^2 - 1)*x + 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + sqrt(x^2 - 1)*x + 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{- x^{2} + x \sqrt{x^{2} - 1} + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-x**2+x*(x**2-1)**(1/2))**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{-x^{2} + \sqrt{x^{2} - 1} x + 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + sqrt(x^2 - 1)*x + 1),x, algorithm="giac")
[Out]