Optimal. Leaf size=10 \[ \frac{F\left (\left .\sin ^{-1}(x)\right |-2\right )}{\sqrt{2}} \]
[Out]
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Rubi [A] time = 0.0273416, antiderivative size = 10, 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 \[ \frac{F\left (\left .\sin ^{-1}(x)\right |-2\right )}{\sqrt{2}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[1 - x^2]*Sqrt[2 + 4*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 5.24884, size = 12, normalized size = 1.2 \[ \frac{\sqrt{2} F\left (\operatorname{asin}{\left (x \right )}\middle | -2\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-x**2+1)**(1/2)/(4*x**2+2)**(1/2),x)
[Out]
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Mathematica [C] time = 0.0512027, size = 58, normalized size = 5.8 \[ -\frac{i \sqrt{1-x^2} \sqrt{2 x^2+1} F\left (i \sinh ^{-1}\left (\sqrt{2} x\right )|-\frac{1}{2}\right )}{2 \sqrt{-2 x^4+x^2+1}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[1 - x^2]*Sqrt[2 + 4*x^2]),x]
[Out]
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Maple [A] time = 0.038, size = 14, normalized size = 1.4 \[{\frac{{\it EllipticF} \left ( x,i\sqrt{2} \right ) \sqrt{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-x^2+1)^(1/2)/(4*x^2+2)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{4 \, x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(4*x^2 + 2)*sqrt(-x^2 + 1)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{4 \, x^{2} + 2} \sqrt{-x^{2} + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(4*x^2 + 2)*sqrt(-x^2 + 1)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{\sqrt{2} \int \frac{1}{\sqrt{- x^{2} + 1} \sqrt{2 x^{2} + 1}}\, dx}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-x**2+1)**(1/2)/(4*x**2+2)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{4 \, x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(4*x^2 + 2)*sqrt(-x^2 + 1)),x, algorithm="giac")
[Out]