Optimal. Leaf size=43 \[ -\frac{5}{21} \sqrt{1-x^4} x-\frac{1}{7} \sqrt{1-x^4} x^5+\frac{5}{21} F\left (\left .\sin ^{-1}(x)\right |-1\right ) \]
[Out]
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Rubi [A] time = 0.0354781, antiderivative size = 43, 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 \[ -\frac{5}{21} \sqrt{1-x^4} x-\frac{1}{7} \sqrt{1-x^4} x^5+\frac{5}{21} F\left (\left .\sin ^{-1}(x)\right |-1\right ) \]
Antiderivative was successfully verified.
[In] Int[x^8/Sqrt[1 - x^4],x]
[Out]
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Rubi in Sympy [A] time = 4.19139, size = 36, normalized size = 0.84 \[ - \frac{x^{5} \sqrt{- x^{4} + 1}}{7} - \frac{5 x \sqrt{- x^{4} + 1}}{21} + \frac{5 F\left (\operatorname{asin}{\left (x \right )}\middle | -1\right )}{21} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**8/(-x**4+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0358736, size = 46, normalized size = 1.07 \[ \frac{3 x^9+2 x^5+5 \sqrt{1-x^4} F\left (\left .\sin ^{-1}(x)\right |-1\right )-5 x}{21 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^8/Sqrt[1 - x^4],x]
[Out]
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Maple [A] time = 0.012, size = 59, normalized size = 1.4 \[ -{\frac{{x}^{5}}{7}\sqrt{-{x}^{4}+1}}-{\frac{5\,x}{21}\sqrt{-{x}^{4}+1}}+{\frac{5\,{\it EllipticF} \left ( x,i \right ) }{21}\sqrt{-{x}^{2}+1}\sqrt{{x}^{2}+1}{\frac{1}{\sqrt{-{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^8/(-x^4+1)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{8}}{\sqrt{-x^{4} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(-x^4 + 1),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{x^{8}}{\sqrt{-x^{4} + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(-x^4 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 2.65064, size = 31, normalized size = 0.72 \[ \frac{x^{9} \Gamma \left (\frac{9}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle |{x^{4} e^{2 i \pi }} \right )}}{4 \Gamma \left (\frac{13}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**8/(-x**4+1)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{8}}{\sqrt{-x^{4} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^8/sqrt(-x^4 + 1),x, algorithm="giac")
[Out]