Optimal. Leaf size=21 \[ \frac{2 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|\frac{1}{6}\right )}{\sqrt{3}} \]
[Out]
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Rubi [A] time = 0.0267, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043 \[ \frac{2 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|\frac{1}{6}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[4 - x^2]/Sqrt[2 - 3*x^2],x]
[Out]
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Rubi in Sympy [A] time = 5.18334, size = 20, normalized size = 0.95 \[ \frac{2 \sqrt{3} E\left (\operatorname{asin}{\left (\frac{\sqrt{6} x}{2} \right )}\middle | \frac{1}{6}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-x**2+4)**(1/2)/(-3*x**2+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0264415, size = 21, normalized size = 1. \[ \frac{2 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|\frac{1}{6}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[4 - x^2]/Sqrt[2 - 3*x^2],x]
[Out]
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Maple [A] time = 0.118, size = 24, normalized size = 1.1 \[{\frac{2\,\sqrt{3}}{3}{\it EllipticE} \left ({\frac{x\sqrt{3}\sqrt{2}}{2}},{\frac{\sqrt{3}\sqrt{2}}{6}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-x^2+4)^(1/2)/(-3*x^2+2)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-x^{2} + 4}}{\sqrt{-3 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 4)/sqrt(-3*x^2 + 2),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{\sqrt{-x^{2} + 4}}{\sqrt{-3 \, x^{2} + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 4)/sqrt(-3*x^2 + 2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- \left (x - 2\right ) \left (x + 2\right )}}{\sqrt{- 3 x^{2} + 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-x**2+4)**(1/2)/(-3*x**2+2)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-x^{2} + 4}}{\sqrt{-3 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-x^2 + 4)/sqrt(-3*x^2 + 2),x, algorithm="giac")
[Out]