Optimal. Leaf size=25 \[ \frac{x}{2 \sqrt{1-x^4}}-\frac{1}{2} F\left (\left .\sin ^{-1}(x)\right |-1\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0207963, 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 \[ \frac{x}{2 \sqrt{1-x^4}}-\frac{1}{2} F\left (\left .\sin ^{-1}(x)\right |-1\right ) \]
Antiderivative was successfully verified.
[In] Int[x^4/(1 - x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.86768, size = 19, normalized size = 0.76 \[ \frac{x}{2 \sqrt{- x^{4} + 1}} - \frac{F\left (\operatorname{asin}{\left (x \right )}\middle | -1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**4/(-x**4+1)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0393378, size = 24, normalized size = 0.96 \[ \frac{1}{2} \left (\frac{x}{\sqrt{1-x^4}}-F\left (\left .\sin ^{-1}(x)\right |-1\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^4/(1 - x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.013, size = 45, normalized size = 1.8 \[{\frac{x}{2}{\frac{1}{\sqrt{-{x}^{4}+1}}}}-{\frac{{\it EllipticF} \left ( x,i \right ) }{2}\sqrt{-{x}^{2}+1}\sqrt{{x}^{2}+1}{\frac{1}{\sqrt{-{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^4/(-x^4+1)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{4}}{{\left (-x^{4} + 1\right )}^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(-x^4 + 1)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (-\frac{x^{4}}{{\left (x^{4} - 1\right )} \sqrt{-x^{4} + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(-x^4 + 1)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.00247, size = 31, normalized size = 1.24 \[ \frac{x^{5} \Gamma \left (\frac{5}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} \frac{5}{4}, \frac{3}{2} \\ \frac{9}{4} \end{matrix}\middle |{x^{4} e^{2 i \pi }} \right )}}{4 \Gamma \left (\frac{9}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**4/(-x**4+1)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{4}}{{\left (-x^{4} + 1\right )}^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^4/(-x^4 + 1)^(3/2),x, algorithm="giac")
[Out]