Optimal. Leaf size=29 \[ \frac{8}{3} F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-1\right )-\frac{1}{3} x \sqrt{16-x^4} \]
[Out]
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Rubi [A] time = 0.0217364, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{8}{3} F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-1\right )-\frac{1}{3} x \sqrt{16-x^4} \]
Antiderivative was successfully verified.
[In] Int[x^4/Sqrt[16 - x^4],x]
[Out]
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Rubi in Sympy [A] time = 3.0727, size = 22, normalized size = 0.76 \[ - \frac{x \sqrt{- x^{4} + 16}}{3} + \frac{8 F\left (\operatorname{asin}{\left (\frac{x}{2} \right )}\middle | -1\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(-x**4+16)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0335157, size = 43, normalized size = 1.48 \[ \frac{x^5+8 \sqrt{16-x^4} F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-1\right )-16 x}{3 \sqrt{16-x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/Sqrt[16 - x^4],x]
[Out]
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Maple [B] time = 0.01, size = 47, normalized size = 1.6 \[ -{\frac{x}{3}\sqrt{-{x}^{4}+16}}+{\frac{8}{3}\sqrt{-{x}^{2}+4}\sqrt{{x}^{2}+4}{\it EllipticF} \left ({\frac{x}{2}},i \right ){\frac{1}{\sqrt{-{x}^{4}+16}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(-x^4+16)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{4}}{\sqrt{-x^{4} + 16}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/sqrt(-x^4 + 16),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{x^{4}}{\sqrt{-x^{4} + 16}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/sqrt(-x^4 + 16),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.99242, size = 32, normalized size = 1.1 \[ \frac{x^{5} \Gamma \left (\frac{5}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle |{\frac{x^{4} e^{2 i \pi }}{16}} \right )}}{16 \Gamma \left (\frac{9}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(-x**4+16)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{4}}{\sqrt{-x^{4} + 16}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/sqrt(-x^4 + 16),x, algorithm="giac")
[Out]