Optimal. Leaf size=53 \[ \frac{x^7}{2 \sqrt{1-x^4}}+\frac{7}{10} \sqrt{1-x^4} x^3+\frac{21}{10} F\left (\left .\sin ^{-1}(x)\right |-1\right )-\frac{21}{10} E\left (\left .\sin ^{-1}(x)\right |-1\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0760235, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 6, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.4 \[ \frac{x^7}{2 \sqrt{1-x^4}}+\frac{7}{10} \sqrt{1-x^4} x^3+\frac{21}{10} F\left (\left .\sin ^{-1}(x)\right |-1\right )-\frac{21}{10} E\left (\left .\sin ^{-1}(x)\right |-1\right ) \]
Antiderivative was successfully verified.
[In] Int[x^10/(1 - x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 12.3158, size = 48, normalized size = 0.91 \[ \frac{x^{7}}{2 \sqrt{- x^{4} + 1}} + \frac{7 x^{3} \sqrt{- x^{4} + 1}}{10} - \frac{21 E\left (\operatorname{asin}{\left (x \right )}\middle | -1\right )}{10} + \frac{21 F\left (\operatorname{asin}{\left (x \right )}\middle | -1\right )}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**10/(-x**4+1)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0639899, size = 49, normalized size = 0.92 \[ \frac{1}{10} \left (-\frac{2 x^7}{\sqrt{1-x^4}}+\frac{7 x^3}{\sqrt{1-x^4}}+21 F\left (\left .\sin ^{-1}(x)\right |-1\right )-21 E\left (\left .\sin ^{-1}(x)\right |-1\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^10/(1 - x^4)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.016, size = 68, normalized size = 1.3 \[{\frac{{x}^{3}}{2}{\frac{1}{\sqrt{-{x}^{4}+1}}}}+{\frac{{x}^{3}}{5}\sqrt{-{x}^{4}+1}}+{\frac{21\,{\it EllipticF} \left ( x,i \right ) -21\,{\it EllipticE} \left ( x,i \right ) }{10}\sqrt{-{x}^{2}+1}\sqrt{{x}^{2}+1}{\frac{1}{\sqrt{-{x}^{4}+1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^10/(-x^4+1)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{10}}{{\left (-x^{4} + 1\right )}^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^10/(-x^4 + 1)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (-\frac{x^{10}}{{\left (x^{4} - 1\right )} \sqrt{-x^{4} + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^10/(-x^4 + 1)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.22732, size = 31, normalized size = 0.58 \[ \frac{x^{11} \Gamma \left (\frac{11}{4}\right ){{}_{2}F_{1}\left (\begin{matrix} \frac{3}{2}, \frac{11}{4} \\ \frac{15}{4} \end{matrix}\middle |{x^{4} e^{2 i \pi }} \right )}}{4 \Gamma \left (\frac{15}{4}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**10/(-x**4+1)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{10}}{{\left (-x^{4} + 1\right )}^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^10/(-x^4 + 1)^(3/2),x, algorithm="giac")
[Out]