Optimal. Leaf size=12 \[ -\sin ^{-1}\left (\frac{1}{4} (-x-1)\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.016483, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\sin ^{-1}\left (\frac{1}{4} (-x-1)\right ) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[15 - 2*x - x^2],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 0.701885, size = 22, normalized size = 1.83 \[ \operatorname{atan}{\left (- \frac{- 2 x - 2}{2 \sqrt{- x^{2} - 2 x + 15}} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-x**2-2*x+15)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00954637, size = 12, normalized size = 1. \[ -\sin ^{-1}\left (\frac{1}{4} (-x-1)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[15 - 2*x - x^2],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.005, size = 7, normalized size = 0.6 \[ \arcsin \left ({\frac{1}{4}}+{\frac{x}{4}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-x^2-2*x+15)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.79663, size = 11, normalized size = 0.92 \[ -\arcsin \left (-\frac{1}{4} \, x - \frac{1}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^2 - 2*x + 15),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.266934, size = 23, normalized size = 1.92 \[ \arctan \left (\frac{x + 1}{\sqrt{-x^{2} - 2 \, x + 15}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^2 - 2*x + 15),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- x^{2} - 2 x + 15}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-x**2-2*x+15)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.268775, size = 8, normalized size = 0.67 \[ \arcsin \left (\frac{1}{4} \, x + \frac{1}{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^2 - 2*x + 15),x, algorithm="giac")
[Out]