Optimal. Leaf size=16 \[ 2 F\left (\left .\sin ^{-1}\left (\frac{\sqrt{x+1}}{2}\right )\right |-4\right ) \]
[Out]
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Rubi [A] time = 0.0379097, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ 2 F\left (\left .\sin ^{-1}\left (\frac{\sqrt{x+1}}{2}\right )\right |-4\right ) \]
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 = 4.0236, size = 14, normalized size = 0.88 \[ 2 F\left (\operatorname{asin}{\left (\frac{\sqrt{x + 1}}{2} \right )}\middle | -4\right ) \]
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 = 0.121041, size = 74, normalized size = 4.62 \[ \frac{i \sqrt{\frac{4}{x-3}+1} \sqrt{\frac{5}{x-3}+1} (x-3)^{3/2} F\left (i \sinh ^{-1}\left (\frac{2}{\sqrt{x-3}}\right )|\frac{5}{4}\right )}{\sqrt{-(x-3) (x+1)} \sqrt{x+2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[3 - x]*Sqrt[1 + x]*Sqrt[2 + x]),x]
[Out]
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Maple [A] time = 0.089, size = 25, normalized size = 1.6 \[ -{1{\it EllipticF} \left ( \sqrt{-1-x},{\frac{i}{2}} \right ) \sqrt{-1-x}{\frac{1}{\sqrt{1+x}}}} \]
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]