Optimal. Leaf size=31 \[ \frac{1}{3} \sqrt{2} F\left (\sin ^{-1}(x)|\frac{3}{2}\right )-\frac{1}{3} \sqrt{2} E\left (\sin ^{-1}(x)|\frac{3}{2}\right ) \]
[Out]
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Rubi [A] time = 0.109574, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.115 \[ \frac{1}{3} \sqrt{2} F\left (\sin ^{-1}(x)|\frac{3}{2}\right )-\frac{1}{3} \sqrt{2} E\left (\sin ^{-1}(x)|\frac{3}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[x^2/(Sqrt[2 - 3*x^2]*Sqrt[1 - x^2]),x]
[Out]
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Rubi in Sympy [A] time = 16.7976, size = 26, normalized size = 0.84 \[ - \frac{\sqrt{2} E\left (\operatorname{asin}{\left (x \right )}\middle | \frac{3}{2}\right )}{3} + \frac{\sqrt{2} F\left (\operatorname{asin}{\left (x \right )}\middle | \frac{3}{2}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(-3*x**2+2)**(1/2)/(-x**2+1)**(1/2),x)
[Out]
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Mathematica [A] time = 0.051221, size = 37, normalized size = 1.19 \[ \frac{F\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|\frac{2}{3}\right )-E\left (\sin ^{-1}\left (\sqrt{\frac{3}{2}} x\right )|\frac{2}{3}\right )}{\sqrt{3}} \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(Sqrt[2 - 3*x^2]*Sqrt[1 - x^2]),x]
[Out]
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Maple [A] time = 0.018, size = 29, normalized size = 0.9 \[{\frac{\sqrt{2}}{3} \left ({\it EllipticF} \left ( x,{\frac{\sqrt{3}\sqrt{2}}{2}} \right ) -{\it EllipticE} \left ( x,{\frac{\sqrt{3}\sqrt{2}}{2}} \right ) \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(-3*x^2+2)^(1/2)/(-x^2+1)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2}}{\sqrt{-x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(sqrt(-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. \[{\rm integral}\left (\frac{x^{2}}{\sqrt{-x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(sqrt(-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. \[ \int \frac{x^{2}}{\sqrt{- \left (x - 1\right ) \left (x + 1\right )} \sqrt{- 3 x^{2} + 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2/(-3*x**2+2)**(1/2)/(-x**2+1)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x^{2}}{\sqrt{-x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(sqrt(-x^2 + 1)*sqrt(-3*x^2 + 2)),x, algorithm="giac")
[Out]