Optimal. Leaf size=31 \[ \frac{1}{3} \sqrt{2} E\left (\sin ^{-1}(x)|-\frac{3}{2}\right )-\frac{1}{3} \sqrt{2} F\left (\sin ^{-1}(x)|-\frac{3}{2}\right ) \]
[Out]
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Rubi [A] time = 0.107223, 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 \[ \frac{1}{3} \sqrt{2} E\left (\sin ^{-1}(x)|-\frac{3}{2}\right )-\frac{1}{3} \sqrt{2} F\left (\sin ^{-1}(x)|-\frac{3}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[x^2/(Sqrt[1 - x^2]*Sqrt[2 + 3*x^2]),x]
[Out]
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Rubi in Sympy [A] time = 16.4008, size = 29, normalized size = 0.94 \[ \frac{\sqrt{2} E\left (\operatorname{asin}{\left (x \right )}\middle | - \frac{3}{2}\right )}{3} - \frac{\sqrt{2} F\left (\operatorname{asin}{\left (x \right )}\middle | - \frac{3}{2}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2/(-x**2+1)**(1/2)/(3*x**2+2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0441813, size = 24, normalized size = 0.77 \[ \frac{1}{3} \sqrt{2} \left (E\left (\sin ^{-1}(x)|-\frac{3}{2}\right )-F\left (\sin ^{-1}(x)|-\frac{3}{2}\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[x^2/(Sqrt[1 - x^2]*Sqrt[2 + 3*x^2]),x]
[Out]
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Maple [A] time = 0.022, size = 31, normalized size = 1. \[ -{\frac{ \left ({\it EllipticF} \left ( x,{\frac{i}{2}}\sqrt{3}\sqrt{2} \right ) -{\it EllipticE} \left ( x,{\frac{i}{2}}\sqrt{3}\sqrt{2} \right ) \right ) \sqrt{2}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2/(-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. \[ \int \frac{x^{2}}{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(sqrt(3*x^2 + 2)*sqrt(-x^2 + 1)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{x^{2}}{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(sqrt(3*x^2 + 2)*sqrt(-x^2 + 1)),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/(-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. \[ \int \frac{x^{2}}{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2/(sqrt(3*x^2 + 2)*sqrt(-x^2 + 1)),x, algorithm="giac")
[Out]