Optimal. Leaf size=25 \[ \frac{1}{3} F\left (\left .\sin ^{-1}(x)\right |-1\right )-\frac{1}{3} x \sqrt{1-x^4} \]
[Out]
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Rubi [A] time = 0.021627, antiderivative size = 25, 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 \[ \frac{1}{3} F\left (\left .\sin ^{-1}(x)\right |-1\right )-\frac{1}{3} x \sqrt{1-x^4} \]
Antiderivative was successfully verified.
[In] Int[x^4/Sqrt[1 - x^4],x]
[Out]
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Rubi in Sympy [A] time = 2.97352, size = 19, normalized size = 0.76 \[ - \frac{x \sqrt{- x^{4} + 1}}{3} + \frac{F\left (\operatorname{asin}{\left (x \right )}\middle | -1\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(-x**4+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0327071, size = 38, normalized size = 1.52 \[ \frac{x^5+\sqrt{1-x^4} F\left (\left .\sin ^{-1}(x)\right |-1\right )-x}{3 \sqrt{1-x^4}} \]
Antiderivative was successfully verified.
[In] Integrate[x^4/Sqrt[1 - x^4],x]
[Out]
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Maple [B] time = 0.011, size = 45, normalized size = 1.8 \[ -{\frac{x}{3}\sqrt{-{x}^{4}+1}}+{\frac{{\it EllipticF} \left ( x,i \right ) }{3}\sqrt{-{x}^{2}+1}\sqrt{{x}^{2}+1}{\frac{1}{\sqrt{-{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(-x^4+1)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{4}}{\sqrt{-x^{4} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/sqrt(-x^4 + 1),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{x^{4}}{\sqrt{-x^{4} + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/sqrt(-x^4 + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 1.91818, size = 31, normalized size = 1.24 \[ \frac{x^{5} \Gamma \left (\frac{5}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle |{x^{4} e^{2 i \pi }} \right )}}{4 \Gamma \left (\frac{9}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(-x**4+1)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{4}}{\sqrt{-x^{4} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/sqrt(-x^4 + 1),x, algorithm="giac")
[Out]