Optimal. Leaf size=25 \[ \frac{2 F\left (\sin ^{-1}\left (\frac{\sqrt{x+2}}{\sqrt{3}}\right )|\frac{3}{5}\right )}{\sqrt{5}} \]
[Out]
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Rubi [A] time = 0.0431427, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038 \[ \frac{2 F\left (\sin ^{-1}\left (\frac{\sqrt{x+2}}{\sqrt{3}}\right )|\frac{3}{5}\right )}{\sqrt{5}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[1 - x]*Sqrt[3 - x]*Sqrt[2 + x]),x]
[Out]
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Rubi in Sympy [A] time = 4.73332, size = 26, normalized size = 1.04 \[ - \sqrt{2} F\left (\operatorname{asin}{\left (\frac{\sqrt{3} \sqrt{- x + 1}}{3} \right )}\middle | - \frac{3}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-x)**(1/2)/(3-x)**(1/2)/(2+x)**(1/2),x)
[Out]
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Mathematica [B] time = 0.0964608, size = 68, normalized size = 2.72 \[ -\frac{2 \sqrt{\frac{x-3}{x-1}} (x-1) \sqrt{\frac{x+2}{x-1}} F\left (\sin ^{-1}\left (\frac{\sqrt{3}}{\sqrt{1-x}}\right )|-\frac{2}{3}\right )}{\sqrt{3} \sqrt{-x^2+x+6}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[1 - x]*Sqrt[3 - x]*Sqrt[2 + x]),x]
[Out]
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Maple [A] time = 0.118, size = 25, normalized size = 1. \[{\frac{2\,\sqrt{3}}{3}{\it EllipticF} \left ({\frac{\sqrt{5}}{5}\sqrt{2+x}},{\frac{\sqrt{5}\sqrt{3}}{3}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-x)^(1/2)/(3-x)^(1/2)/(2+x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x + 2} \sqrt{-x + 3} \sqrt{-x + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 2)*sqrt(-x + 3)*sqrt(-x + 1)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{x + 2} \sqrt{-x + 3} \sqrt{-x + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 2)*sqrt(-x + 3)*sqrt(-x + 1)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- x + 1} \sqrt{- x + 3} \sqrt{x + 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-x)**(1/2)/(3-x)**(1/2)/(2+x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x + 2} \sqrt{-x + 3} \sqrt{-x + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 2)*sqrt(-x + 3)*sqrt(-x + 1)),x, algorithm="giac")
[Out]