Optimal. Leaf size=14 \[ -2 F\left (\left .\sin ^{-1}\left (\sqrt{4-x}\right )\right |-1\right ) \]
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Rubi [A] time = 0.0649002, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.13 \[ -2 F\left (\left .\sin ^{-1}\left (\sqrt{4-x}\right )\right |-1\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[4 - x]*Sqrt[(5 - x)*(-3 + x)]),x]
[Out]
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Rubi in Sympy [A] time = 8.49995, size = 14, normalized size = 1. \[ - 2 F\left (\operatorname{asin}{\left (\sqrt{- x + 4} \right )}\middle | -1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(4-x)**(1/2)/((5-x)*(-3+x))**(1/2),x)
[Out]
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Mathematica [B] time = 0.0248544, size = 46, normalized size = 3.29 \[ \frac{2 \sqrt{-x^2+8 x-15} F\left (\left .\sin ^{-1}\left (\frac{1}{\sqrt{4-x}}\right )\right |-1\right )}{\sqrt{1-\frac{1}{(x-4)^2}} (x-4)} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[4 - x]*Sqrt[(5 - x)*(-3 + x)]),x]
[Out]
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Maple [B] time = 0.023, size = 35, normalized size = 2.5 \[ -2\,{\frac{{\it EllipticF} \left ( \sqrt{4-x},i \right ) \sqrt{5-x}\sqrt{-3+x}}{\sqrt{- \left ( -5+x \right ) \left ( -3+x \right ) }}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(4-x)^(1/2)/((5-x)*(-3+x))^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-{\left (x - 3\right )}{\left (x - 5\right )}} \sqrt{-x + 4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-(x - 3)*(x - 5))*sqrt(-x + 4)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{-x^{2} + 8 \, x - 15} \sqrt{-x + 4}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-(x - 3)*(x - 5))*sqrt(-x + 4)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- \left (x - 5\right ) \left (x - 3\right )} \sqrt{- x + 4}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(4-x)**(1/2)/((5-x)*(-3+x))**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-{\left (x - 3\right )}{\left (x - 5\right )}} \sqrt{-x + 4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-(x - 3)*(x - 5))*sqrt(-x + 4)),x, algorithm="giac")
[Out]