Optimal. Leaf size=35 \[ \frac{7}{3} \sqrt{2} F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-6\right )-\frac{1}{3} \sqrt{2} E\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-6\right ) \]
[Out]
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Rubi [A] time = 0.0670297, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13 \[ \frac{7}{3} \sqrt{2} F\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-6\right )-\frac{1}{3} \sqrt{2} E\left (\left .\sin ^{-1}\left (\frac{x}{2}\right )\right |-6\right ) \]
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 = 12.424, size = 31, normalized size = 0.89 \[ - \frac{\sqrt{2} E\left (\operatorname{asin}{\left (\frac{x}{2} \right )}\middle | -6\right )}{3} + \frac{7 \sqrt{2} F\left (\operatorname{asin}{\left (\frac{x}{2} \right )}\middle | -6\right )}{3} \]
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 [C] time = 0.0267695, size = 27, normalized size = 0.77 \[ -\frac{2 i E\left (i \sinh ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|-\frac{1}{6}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[4 - x^2]/Sqrt[2 + 3*x^2],x]
[Out]
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Maple [A] time = 0.035, size = 37, normalized size = 1.1 \[{\frac{\sqrt{2}}{3} \left ( 7\,{\it EllipticF} \left ( x/2,i\sqrt{3}\sqrt{2} \right ) -{\it EllipticE} \left ({\frac{x}{2}},i\sqrt{3}\sqrt{2} \right ) \right ) } \]
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]