Optimal. Leaf size=14 \[ -2 F\left (\left .\sin ^{-1}\left (\sqrt{4-x}\right )\right |-1\right ) \]
[Out]
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Rubi [A] time = 0.0344033, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ -2 F\left (\left .\sin ^{-1}\left (\sqrt{4-x}\right )\right |-1\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[4 - x]*Sqrt[-15 + 8*x - x^2]),x]
[Out]
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Rubi in Sympy [A] time = 7.60024, 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)/(-x**2+8*x-15)**(1/2),x)
[Out]
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Mathematica [B] time = 0.0697016, size = 44, normalized size = 3.14 \[ -\frac{2 \sqrt{1-\frac{1}{(x-4)^2}} (x-4) F\left (\left .\sin ^{-1}\left (\frac{1}{\sqrt{4-x}}\right )\right |-1\right )}{\sqrt{-x^2+8 x-15}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[4 - x]*Sqrt[-15 + 8*x - x^2]),x]
[Out]
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Maple [B] time = 0.017, size = 47, normalized size = 3.4 \[ 2\,{\frac{{\it EllipticF} \left ( \sqrt{4-x},i \right ) \sqrt{-3+x}\sqrt{5-x}\sqrt{-{x}^{2}+8\,x-15}}{{x}^{2}-8\,x+15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(4-x)^(1/2)/(-x^2+8*x-15)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-x^{2} + 8 \, x - 15} \sqrt{-x + 4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^2 + 8*x - 15)*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^2 + 8*x - 15)*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)/(-x**2+8*x-15)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-x^{2} + 8 \, x - 15} \sqrt{-x + 4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-x^2 + 8*x - 15)*sqrt(-x + 4)),x, algorithm="giac")
[Out]