Optimal. Leaf size=57 \[ -\frac{2 \sqrt{x+1} \sqrt{x+3} F\left (\sin ^{-1}\left (\frac{1}{\sqrt{\frac{x}{5}+\frac{3}{5}}}\right )|\frac{2}{5}\right )}{\sqrt{5} \sqrt{-x-3} \sqrt{-x-1}} \]
[Out]
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Rubi [A] time = 0.118975, antiderivative size = 57, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{2 \sqrt{x+1} \sqrt{x+3} F\left (\sin ^{-1}\left (\frac{1}{\sqrt{\frac{x}{5}+\frac{3}{5}}}\right )|\frac{2}{5}\right )}{\sqrt{5} \sqrt{-x-3} \sqrt{-x-1}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[-3 - x]*Sqrt[-1 - x]*Sqrt[-2 + x]),x]
[Out]
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Rubi in Sympy [A] time = 9.63543, size = 65, normalized size = 1.14 \[ - \frac{2 \sqrt{2} \sqrt{- \frac{x}{3} + \frac{2}{3}} \sqrt{\frac{x}{2} + \frac{3}{2}} F\left (\operatorname{asin}{\left (\frac{\sqrt{2} \sqrt{- x - 1}}{2} \right )}\middle | - \frac{2}{3}\right )}{\sqrt{- x - 3} \sqrt{x - 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-3-x)**(1/2)/(-1-x)**(1/2)/(-2+x)**(1/2),x)
[Out]
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Mathematica [C] time = 0.0534599, size = 75, normalized size = 1.32 \[ \frac{2 i \sqrt{\frac{3}{x-2}+1} \sqrt{\frac{5}{x-2}+1} (x-2) F\left (i \sinh ^{-1}\left (\frac{\sqrt{3}}{\sqrt{x-2}}\right )|\frac{5}{3}\right )}{\sqrt{-3 (x-2)-15} \sqrt{-x-1}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[-3 - x]*Sqrt[-1 - x]*Sqrt[-2 + x]),x]
[Out]
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Maple [C] time = 0.054, size = 57, normalized size = 1. \[{\frac{2\,\sqrt{3}}{3\,{x}^{2}+3\,x-18}{\it EllipticF} \left ({\frac{1}{2}\sqrt{-2-2\,x}},{\frac{i}{3}}\sqrt{3}\sqrt{2} \right ) \sqrt{3+x}\sqrt{2-x}\sqrt{-2+x}\sqrt{-3-x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-3-x)^(1/2)/(-1-x)^(1/2)/(-2+x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x - 2} \sqrt{-x - 1} \sqrt{-x - 3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 2)*sqrt(-x - 1)*sqrt(-x - 3)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{x - 2} \sqrt{-x - 1} \sqrt{-x - 3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 2)*sqrt(-x - 1)*sqrt(-x - 3)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- x - 3} \sqrt{- x - 1} \sqrt{x - 2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-3-x)**(1/2)/(-1-x)**(1/2)/(-2+x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x - 2} \sqrt{-x - 1} \sqrt{-x - 3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 2)*sqrt(-x - 1)*sqrt(-x - 3)),x, algorithm="giac")
[Out]