Optimal. Leaf size=38 \[ \sqrt{\frac{2}{3}} \sqrt{1-4 x^4} x+\frac{2 F\left (\left .\sin ^{-1}\left (\sqrt{2} x\right )\right |-1\right )}{\sqrt{3}} \]
[Out]
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Rubi [A] time = 0.0347745, antiderivative size = 38, 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 \[ \sqrt{\frac{2}{3}} \sqrt{1-4 x^4} x+\frac{2 F\left (\left .\sin ^{-1}\left (\sqrt{2} x\right )\right |-1\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[3 - 6*x^2]*Sqrt[2 + 4*x^2],x]
[Out]
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Rubi in Sympy [A] time = 5.06177, size = 32, normalized size = 0.84 \[ \frac{x \sqrt{- 24 x^{4} + 6}}{3} + \frac{2 \sqrt{3} F\left (\operatorname{asin}{\left (\sqrt{2} x \right )}\middle | -1\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((-6*x**2+3)**(1/2)*(4*x**2+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0803951, size = 32, normalized size = 0.84 \[ \frac{\sqrt{2-8 x^4} x+2 F\left (\left .\sin ^{-1}\left (\sqrt{2} x\right )\right |-1\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[3 - 6*x^2]*Sqrt[2 + 4*x^2],x]
[Out]
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Maple [B] time = 0.059, size = 75, normalized size = 2. \[ -{\frac{\sqrt{2}}{36\,{x}^{4}-9}\sqrt{-6\,{x}^{2}+3}\sqrt{2\,{x}^{2}+1} \left ( \sqrt{2}\sqrt{3}\sqrt{-6\,{x}^{2}+3}\sqrt{2\,{x}^{2}+1}{\it EllipticF} \left ( x\sqrt{2},i \right ) -12\,{x}^{5}+3\,x \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((-6*x^2+3)^(1/2)*(4*x^2+2)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{4 \, x^{2} + 2} \sqrt{-6 \, x^{2} + 3}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 + 2)*sqrt(-6*x^2 + 3),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\sqrt{4 \, x^{2} + 2} \sqrt{-6 \, x^{2} + 3}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 + 2)*sqrt(-6*x^2 + 3),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \sqrt{6} \int \sqrt{- 2 x^{2} + 1} \sqrt{2 x^{2} + 1}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-6*x**2+3)**(1/2)*(4*x**2+2)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \sqrt{4 \, x^{2} + 2} \sqrt{-6 \, x^{2} + 3}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(4*x^2 + 2)*sqrt(-6*x^2 + 3),x, algorithm="giac")
[Out]