Optimal. Leaf size=10 \[ F\left (\left .\sin ^{-1}\left (\frac{x}{\sqrt{2}}\right )\right |-6\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0408244, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ F\left (\left .\sin ^{-1}\left (\frac{x}{\sqrt{2}}\right )\right |-6\right ) \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[2 + 5*x^2 - 3*x^4],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 7.77856, size = 12, normalized size = 1.2 \[ F\left (\operatorname{asin}{\left (\frac{\sqrt{2} x}{2} \right )}\middle | -6\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-3*x**4+5*x**2+2)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.0401972, size = 65, normalized size = 6.5 \[ -\frac{i \sqrt{1-\frac{x^2}{2}} \sqrt{3 x^2+1} F\left (i \sinh ^{-1}\left (\sqrt{3} x\right )|-\frac{1}{6}\right )}{\sqrt{3} \sqrt{-3 x^4+5 x^2+2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[2 + 5*x^2 - 3*x^4],x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0., size = 51, normalized size = 5.1 \[{\frac{\sqrt{2}}{2}\sqrt{-2\,{x}^{2}+4}\sqrt{3\,{x}^{2}+1}{\it EllipticF} \left ({\frac{\sqrt{2}x}{2}},i\sqrt{6} \right ){\frac{1}{\sqrt{-3\,{x}^{4}+5\,{x}^{2}+2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-3*x^4+5*x^2+2)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-3 \, x^{4} + 5 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-3*x^4 + 5*x^2 + 2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{-3 \, x^{4} + 5 \, x^{2} + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-3*x^4 + 5*x^2 + 2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- 3 x^{4} + 5 x^{2} + 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-3*x**4+5*x**2+2)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-3 \, x^{4} + 5 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-3*x^4 + 5*x^2 + 2),x, algorithm="giac")
[Out]