Optimal. Leaf size=2 \[ \sinh ^{-1}(x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00396203, antiderivative size = 2, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111 \[ \sinh ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[1 + x^2],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 0.088769, size = 2, normalized size = 1. \[ \operatorname{asinh}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(x**2+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00512549, size = 2, normalized size = 1. \[ \sinh ^{-1}(x) \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[1 + x^2],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 3, normalized size = 1.5 \[{\it Arcsinh} \left ( x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(x^2+1)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.798872, size = 3, normalized size = 1.5 \[ \operatorname{arsinh}\left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(x^2 + 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.266181, size = 19, normalized size = 9.5 \[ -\log \left (-x + \sqrt{x^{2} + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(x^2 + 1),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.280099, size = 2, normalized size = 1. \[ \operatorname{asinh}{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x**2+1)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.263489, size = 19, normalized size = 9.5 \[ -{\rm ln}\left (-x + \sqrt{x^{2} + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(x^2 + 1),x, algorithm="giac")
[Out]