Optimal. Leaf size=12 \[ \frac{1}{2} \sin ^{-1}\left (\frac{x^2}{4}\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.014869, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{1}{2} \sin ^{-1}\left (\frac{x^2}{4}\right ) \]
Antiderivative was successfully verified.
[In] Int[x/Sqrt[16 - x^4],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.54564, size = 7, normalized size = 0.58 \[ \frac{\operatorname{asin}{\left (\frac{x^{2}}{4} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(-x**4+16)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00853491, size = 12, normalized size = 1. \[ \frac{1}{2} \sin ^{-1}\left (\frac{x^2}{4}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x/Sqrt[16 - x^4],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.01, size = 9, normalized size = 0.8 \[{\frac{1}{2}\arcsin \left ({\frac{{x}^{2}}{4}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(-x^4+16)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.60151, size = 22, normalized size = 1.83 \[ -\frac{1}{2} \, \arctan \left (\frac{\sqrt{-x^{4} + 16}}{x^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(-x^4 + 16),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.254795, size = 24, normalized size = 2. \[ -\arctan \left (\frac{\sqrt{-x^{4} + 16} - 4}{x^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(-x^4 + 16),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 3.3181, size = 24, normalized size = 2. \[ \begin{cases} - \frac{i \operatorname{acosh}{\left (\frac{x^{2}}{4} \right )}}{2} & \text{for}\: \frac{\left |{x^{4}}\right |}{16} > 1 \\\frac{\operatorname{asin}{\left (\frac{x^{2}}{4} \right )}}{2} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-x**4+16)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.221435, size = 11, normalized size = 0.92 \[ \frac{1}{2} \, \arcsin \left (\frac{1}{4} \, x^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(-x^4 + 16),x, algorithm="giac")
[Out]