Optimal. Leaf size=13 \[ -\frac{2}{3} (1-x)^{3/2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00614335, antiderivative size = 13, 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 \[ -\frac{2}{3} (1-x)^{3/2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - x^2]/Sqrt[1 + x],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.24227, size = 10, normalized size = 0.77 \[ - \frac{2 \left (- x + 1\right )^{\frac{3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x**2+1)**(1/2)/(1+x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0110106, size = 25, normalized size = 1.92 \[ \frac{2 (x-1) \sqrt{1-x^2}}{3 \sqrt{x+1}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - x^2]/Sqrt[1 + x],x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.003, size = 20, normalized size = 1.5 \[{\frac{2\,x-2}{3}\sqrt{-{x}^{2}+1}{\frac{1}{\sqrt{1+x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^2+1)^(1/2)/(1+x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.691604, size = 16, normalized size = 1.23 \[ \frac{2}{3} \,{\left (x - 1\right )} \sqrt{-x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 1)/sqrt(x + 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.265076, size = 39, normalized size = 3. \[ -\frac{2 \,{\left (x^{3} - x^{2} - x + 1\right )}}{3 \, \sqrt{-x^{2} + 1} \sqrt{x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 1)/sqrt(x + 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- \left (x - 1\right ) \left (x + 1\right )}}{\sqrt{x + 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**2+1)**(1/2)/(1+x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.267156, size = 20, normalized size = 1.54 \[ -\frac{2}{3} \,{\left (-x + 1\right )}^{\frac{3}{2}} + \frac{4}{3} \, \sqrt{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 1)/sqrt(x + 1),x, algorithm="giac")
[Out]