Optimal. Leaf size=20 \[ \frac{E\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|-\frac{2}{3}\right )}{\sqrt{3}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0238563, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{E\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|-\frac{2}{3}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 + x^2]/Sqrt[2 - 3*x^2],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.1441, size = 20, normalized size = 1. \[ \frac{\sqrt{3} E\left (\operatorname{asin}{\left (\frac{\sqrt{6} x}{2} \right )}\middle | - \frac{2}{3}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((x**2+1)**(1/2)/(-3*x**2+2)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0254786, size = 20, normalized size = 1. \[ \frac{E\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|-\frac{2}{3}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 + x^2]/Sqrt[2 - 3*x^2],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.028, size = 25, normalized size = 1.3 \[{\frac{\sqrt{3}}{3}{\it EllipticE} \left ({\frac{x\sqrt{3}\sqrt{2}}{2}},{\frac{i}{3}}\sqrt{3}\sqrt{2} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x^{2} + 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^2 + 1)/sqrt(-3*x^2 + 2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{\sqrt{x^{2} + 1}}{\sqrt{-3 \, x^{2} + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^2 + 1)/sqrt(-3*x^2 + 2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x^{2} + 1}}{\sqrt{- 3 x^{2} + 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((x**2+1)**(1/2)/(-3*x**2+2)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{x^{2} + 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(x^2 + 1)/sqrt(-3*x^2 + 2),x, algorithm="giac")
[Out]