Optimal. Leaf size=19 \[ -\frac{E\left (\left .\cos ^{-1}\left (\sqrt{\frac{3}{2}} x\right )\right |2\right )}{\sqrt{3}} \]
[Out]
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Rubi [A] time = 0.0261532, antiderivative size = 19, 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 \[ -\frac{E\left (\left .\cos ^{-1}\left (\sqrt{\frac{3}{2}} x\right )\right |2\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[-1 + 3*x^2]/Sqrt[2 - 3*x^2],x]
[Out]
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Rubi in Sympy [A] time = 5.26547, size = 19, normalized size = 1. \[ - \frac{\sqrt{3} E\left (\operatorname{acos}{\left (\frac{\sqrt{6} x}{2} \right )}\middle | 2\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3*x**2-1)**(1/2)/(-3*x**2+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0353428, size = 35, normalized size = 1.84 \[ \frac{\sqrt{3 x^2-1} E\left (\left .\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )\right |2\right )}{\sqrt{3-9 x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[-1 + 3*x^2]/Sqrt[2 - 3*x^2],x]
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Maple [A] time = 0.027, size = 37, normalized size = 2. \[ -{\frac{\sqrt{3}}{3}{\it EllipticE} \left ({\frac{x\sqrt{3}\sqrt{2}}{2}},\sqrt{2} \right ) \sqrt{-3\,{x}^{2}+1}{\frac{1}{\sqrt{3\,{x}^{2}-1}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{3 \, x^{2} - 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(3*x^2 - 1)/sqrt(-3*x^2 + 2),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{\sqrt{3 \, x^{2} - 1}}{\sqrt{-3 \, x^{2} + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(3*x^2 - 1)/sqrt(-3*x^2 + 2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{3 x^{2} - 1}}{\sqrt{- 3 x^{2} + 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x**2-1)**(1/2)/(-3*x**2+2)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{3 \, x^{2} - 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(3*x^2 - 1)/sqrt(-3*x^2 + 2),x, algorithm="giac")
[Out]