Optimal. Leaf size=57 \[ -\frac{\sqrt{x+3} F\left (\sin ^{-1}\left (\frac{2}{\sqrt{x+3}}\right )|\frac{5}{4}\right )}{\sqrt{-x-3}}-\frac{i K\left (-\frac{1}{4}\right ) \sqrt{x+3}}{\sqrt{-x-3}} \]
[Out]
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Rubi [A] time = 0.0717495, antiderivative size = 36, normalized size of antiderivative = 0.63, number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ -\frac{\sqrt{x+3} F\left (\sin ^{-1}\left (\frac{1}{\sqrt{\frac{x}{4}+\frac{3}{4}}}\right )|\frac{5}{4}\right )}{\sqrt{-x-3}} \]
Warning: Unable to verify antiderivative.
[In] Int[1/(Sqrt[-3 - x]*Sqrt[-2 + x]*Sqrt[-1 + x]),x]
[Out]
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Rubi in Sympy [A] time = 8.15629, size = 46, normalized size = 0.81 \[ \frac{2 \sqrt{- x + 2} \sqrt{\frac{x}{4} + \frac{3}{4}} F\left (\operatorname{asin}{\left (\sqrt{x - 1} \right )}\middle | - \frac{1}{4}\right )}{\sqrt{- x - 3} \sqrt{x - 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-3-x)**(1/2)/(-2+x)**(1/2)/(-1+x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.136148, size = 63, normalized size = 1.11 \[ \frac{i \sqrt{\frac{x-2}{x-1}} \sqrt{\frac{x-1}{x+3}} F\left (i \sinh ^{-1}\left (\frac{2}{\sqrt{-x-3}}\right )|\frac{5}{4}\right )}{\sqrt{\frac{x-2}{x+3}}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[-3 - x]*Sqrt[-2 + x]*Sqrt[-1 + x]),x]
[Out]
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Maple [A] time = 0.059, size = 66, normalized size = 1.2 \[{\frac{1}{-{x}^{3}+7\,x-6}\sqrt{-3-x}\sqrt{-2+x}\sqrt{-1+x}\sqrt{3+x}\sqrt{1-x}\sqrt{2-x}{\it EllipticF} \left ({\frac{\sqrt{5}}{5}\sqrt{3+x}},{\frac{\sqrt{5}}{2}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-3-x)^(1/2)/(-2+x)^(1/2)/(-1+x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x - 1} \sqrt{x - 2} \sqrt{-x - 3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 1)*sqrt(x - 2)*sqrt(-x - 3)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{x - 1} \sqrt{x - 2} \sqrt{-x - 3}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 1)*sqrt(x - 2)*sqrt(-x - 3)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- x - 3} \sqrt{x - 2} \sqrt{x - 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-3-x)**(1/2)/(-2+x)**(1/2)/(-1+x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x - 1} \sqrt{x - 2} \sqrt{-x - 3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 1)*sqrt(x - 2)*sqrt(-x - 3)),x, algorithm="giac")
[Out]