Optimal. Leaf size=45 \[ -\frac{\sqrt{1-x^4}}{7 x^7}-\frac{5 \sqrt{1-x^4}}{21 x^3}+\frac{5}{21} F\left (\left .\sin ^{-1}(x)\right |-1\right ) \]
[Out]
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Rubi [A] time = 0.0358512, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ -\frac{\sqrt{1-x^4}}{7 x^7}-\frac{5 \sqrt{1-x^4}}{21 x^3}+\frac{5}{21} F\left (\left .\sin ^{-1}(x)\right |-1\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(x^8*Sqrt[1 - x^4]),x]
[Out]
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Rubi in Sympy [A] time = 4.06708, size = 37, normalized size = 0.82 \[ \frac{5 F\left (\operatorname{asin}{\left (x \right )}\middle | -1\right )}{21} - \frac{5 \sqrt{- x^{4} + 1}}{21 x^{3}} - \frac{\sqrt{- x^{4} + 1}}{7 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**8/(-x**4+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0359872, size = 50, normalized size = 1.11 \[ \frac{5 x^8-2 x^4+5 \sqrt{1-x^4} x^7 F\left (\left .\sin ^{-1}(x)\right |-1\right )-3}{21 x^7 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^8*Sqrt[1 - x^4]),x]
[Out]
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Maple [A] time = 0.018, size = 61, normalized size = 1.4 \[ -{\frac{1}{7\,{x}^{7}}\sqrt{-{x}^{4}+1}}-{\frac{5}{21\,{x}^{3}}\sqrt{-{x}^{4}+1}}+{\frac{5\,{\it EllipticF} \left ( x,i \right ) }{21}\sqrt{-{x}^{2}+1}\sqrt{{x}^{2}+1}{\frac{1}{\sqrt{-{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^8/(-x^4+1)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-x^{4} + 1} x^{8}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 1)*x^8),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{-x^{4} + 1} x^{8}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 1)*x^8),x, algorithm="fricas")
[Out]
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Sympy [A] time = 3.72186, size = 37, normalized size = 0.82 \[ \frac{\Gamma \left (- \frac{7}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} - \frac{7}{4}, \frac{1}{2} \\ - \frac{3}{4} \end{matrix}\middle |{x^{4} e^{2 i \pi }} \right )}}{4 x^{7} \Gamma \left (- \frac{3}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**8/(-x**4+1)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-x^{4} + 1} x^{8}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^4 + 1)*x^8),x, algorithm="giac")
[Out]