Optimal. Leaf size=18 \[ \sqrt{2} F\left (\sin ^{-1}\left (\sqrt{x-3}\right )|\frac{1}{2}\right ) \]
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Rubi [A] time = 0.0423021, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038 \[ \sqrt{2} F\left (\sin ^{-1}\left (\sqrt{x-3}\right )|\frac{1}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[4 - x]*Sqrt[5 - x]*Sqrt[-3 + x]),x]
[Out]
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Rubi in Sympy [A] time = 4.55227, size = 15, normalized size = 0.83 \[ \sqrt{2} F\left (\operatorname{asin}{\left (\sqrt{x - 3} \right )}\middle | \frac{1}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(4-x)**(1/2)/(5-x)**(1/2)/(-3+x)**(1/2),x)
[Out]
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Mathematica [B] time = 0.137452, size = 46, normalized size = 2.56 \[ \frac{2 \sqrt{-x^2+8 x-15} F\left (\left .\sin ^{-1}\left (\frac{1}{\sqrt{4-x}}\right )\right |-1\right )}{\sqrt{1-\frac{1}{(x-4)^2}} (x-4)} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[4 - x]*Sqrt[5 - x]*Sqrt[-3 + x]),x]
[Out]
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Maple [C] time = 0.085, size = 13, normalized size = 0.7 \[ -2\,{\it EllipticF} \left ( \sqrt{4-x},i \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(4-x)^(1/2)/(5-x)^(1/2)/(-3+x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x - 3} \sqrt{-x + 5} \sqrt{-x + 4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 3)*sqrt(-x + 5)*sqrt(-x + 4)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{x - 3} \sqrt{-x + 5} \sqrt{-x + 4}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 3)*sqrt(-x + 5)*sqrt(-x + 4)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 13.0654, size = 66, normalized size = 3.67 \[ \frac{{G_{6, 6}^{5, 3}\left (\begin{matrix} \frac{1}{2}, 1, 1 & \frac{3}{4}, \frac{3}{4}, \frac{5}{4} \\\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4} & 0 \end{matrix} \middle |{\frac{1}{\left (x - 4\right )^{2}}} \right )}}{4 \pi ^{\frac{3}{2}}} - \frac{{G_{6, 6}^{3, 5}\left (\begin{matrix} - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4} & 1 \\0, \frac{1}{2}, 0 & - \frac{1}{4}, \frac{1}{4}, \frac{1}{4} \end{matrix} \middle |{\frac{e^{- 2 i \pi }}{\left (x - 4\right )^{2}}} \right )}}{4 \pi ^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(4-x)**(1/2)/(5-x)**(1/2)/(-3+x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x - 3} \sqrt{-x + 5} \sqrt{-x + 4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x - 3)*sqrt(-x + 5)*sqrt(-x + 4)),x, algorithm="giac")
[Out]