Optimal. Leaf size=43 \[ \frac{2 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|-\frac{1}{6}\right )}{\sqrt{3}}-\frac{2 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|-\frac{1}{6}\right )}{\sqrt{3}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.100589, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{2 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|-\frac{1}{6}\right )}{\sqrt{3}}-\frac{2 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|-\frac{1}{6}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[x^2/(Sqrt[2 - 3*x^2]*Sqrt[4 + x^2]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 15.5012, size = 46, normalized size = 1.07 \[ \frac{2 \sqrt{3} E\left (\operatorname{asin}{\left (\frac{\sqrt{6} x}{2} \right )}\middle | - \frac{1}{6}\right )}{3} - \frac{2 \sqrt{3} F\left (\operatorname{asin}{\left (\frac{\sqrt{6} x}{2} \right )}\middle | - \frac{1}{6}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(-3*x**2+2)**(1/2)/(x**2+4)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0419968, size = 38, normalized size = 0.88 \[ \frac{2 \left (E\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|-\frac{1}{6}\right )-F\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|-\frac{1}{6}\right )\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(Sqrt[2 - 3*x^2]*Sqrt[4 + x^2]),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.027, size = 47, normalized size = 1.1 \[ -{\frac{2\,\sqrt{3}}{3} \left ({\it EllipticF} \left ({\frac{x\sqrt{3}\sqrt{2}}{2}},{\frac{i}{6}}\sqrt{3}\sqrt{2} \right ) -{\it EllipticE} \left ({\frac{x\sqrt{3}\sqrt{2}}{2}},{\frac{i}{6}}\sqrt{3}\sqrt{2} \right ) \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(-3*x^2+2)^(1/2)/(x^2+4)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2}}{\sqrt{x^{2} + 4} \sqrt{-3 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(sqrt(x^2 + 4)*sqrt(-3*x^2 + 2)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{x^{2}}{\sqrt{x^{2} + 4} \sqrt{-3 \, x^{2} + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(sqrt(x^2 + 4)*sqrt(-3*x^2 + 2)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2}}{\sqrt{- 3 x^{2} + 2} \sqrt{x^{2} + 4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(-3*x**2+2)**(1/2)/(x**2+4)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2}}{\sqrt{x^{2} + 4} \sqrt{-3 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(sqrt(x^2 + 4)*sqrt(-3*x^2 + 2)),x, algorithm="giac")
[Out]