Optimal. Leaf size=31 \[ \frac{1}{96} F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-1\right )-\frac{\sqrt{16-x^4}}{48 x^3} \]
[Out]
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Rubi [A] time = 0.0217035, antiderivative size = 31, 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 \[ \frac{1}{96} F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-1\right )-\frac{\sqrt{16-x^4}}{48 x^3} \]
Antiderivative was successfully verified.
[In] Int[1/(x^4*Sqrt[16 - x^4]),x]
[Out]
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Rubi in Sympy [A] time = 2.94358, size = 22, normalized size = 0.71 \[ \frac{F\left (\operatorname{asin}{\left (\frac{x}{2} \right )}\middle | -1\right )}{96} - \frac{\sqrt{- x^{4} + 16}}{48 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**4/(-x**4+16)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0363894, size = 48, normalized size = 1.55 \[ \frac{2 x^4+\sqrt{16-x^4} x^3 F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-1\right )-32}{96 x^3 \sqrt{16-x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^4*Sqrt[16 - x^4]),x]
[Out]
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Maple [B] time = 0.016, size = 49, normalized size = 1.6 \[ -{\frac{1}{48\,{x}^{3}}\sqrt{-{x}^{4}+16}}+{\frac{1}{96}\sqrt{-{x}^{2}+4}\sqrt{{x}^{2}+4}{\it EllipticF} \left ({\frac{x}{2}},i \right ){\frac{1}{\sqrt{-{x}^{4}+16}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^4/(-x^4+16)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-x^{4} + 16} x^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 16)*x^4),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{-x^{4} + 16} x^{4}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 16)*x^4),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.36044, size = 36, normalized size = 1.16 \[ \frac{\Gamma \left (- \frac{3}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle |{\frac{x^{4} e^{2 i \pi }}{16}} \right )}}{16 x^{3} \Gamma \left (\frac{1}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**4/(-x**4+16)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-x^{4} + 16} x^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 16)*x^4),x, algorithm="giac")
[Out]