Optimal. Leaf size=6 \[ \sin ^{-1}\left (\frac{x}{4}\right ) \]
[Out]
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Rubi [A] time = 0.00402379, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \sin ^{-1}\left (\frac{x}{4}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[16 - x^2],x]
[Out]
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Rubi in Sympy [A] time = 0.528762, size = 3, normalized size = 0.5 \[ \operatorname{asin}{\left (\frac{x}{4} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-x**2+16)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00652445, size = 6, normalized size = 1. \[ \sin ^{-1}\left (\frac{x}{4}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[16 - x^2],x]
[Out]
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Maple [A] time = 0.005, size = 5, normalized size = 0.8 \[ \arcsin \left ({\frac{x}{4}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-x^2+16)^(1/2),x)
[Out]
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Maxima [A] time = 1.49938, size = 5, normalized size = 0.83 \[ \arcsin \left (\frac{1}{4} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^2 + 16),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.22106, size = 24, normalized size = 4. \[ -2 \, \arctan \left (\frac{\sqrt{-x^{2} + 16} - 4}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^2 + 16),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.154797, size = 3, normalized size = 0.5 \[ \operatorname{asin}{\left (\frac{x}{4} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-x**2+16)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.219416, size = 5, normalized size = 0.83 \[ \arcsin \left (\frac{1}{4} \, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^2 + 16),x, algorithm="giac")
[Out]