Optimal. Leaf size=12 \[ \frac{1}{2} F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-1\right ) \]
[Out]
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Rubi [A] time = 0.00638878, antiderivative size = 12, 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 \[ \frac{1}{2} F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-1\right ) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[16 - x^4],x]
[Out]
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Rubi in Sympy [A] time = 1.03983, size = 8, normalized size = 0.67 \[ \frac{F\left (\operatorname{asin}{\left (\frac{x}{2} \right )}\middle | -1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-x**4+16)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0209384, size = 12, normalized size = 1. \[ \frac{1}{2} F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-1\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[16 - x^4],x]
[Out]
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Maple [B] time = 0.007, size = 34, normalized size = 2.8 \[{\frac{1}{2}\sqrt{-{x}^{2}+4}\sqrt{{x}^{2}+4}{\it EllipticF} \left ({\frac{x}{2}},i \right ){\frac{1}{\sqrt{-{x}^{4}+16}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-x^4+16)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-x^{4} + 16}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^4 + 16),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{-x^{4} + 16}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^4 + 16),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.73025, size = 31, normalized size = 2.58 \[ \frac{x \Gamma \left (\frac{1}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle |{\frac{x^{4} e^{2 i \pi }}{16}} \right )}}{16 \Gamma \left (\frac{5}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-x**4+16)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-x^{4} + 16}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-x^4 + 16),x, algorithm="giac")
[Out]