Optimal. Leaf size=25 \[ -\frac{2 F\left (\sin ^{-1}\left (\frac{\sqrt{6-x}}{2}\right )|\frac{4}{5}\right )}{\sqrt{5}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0866572, antiderivative size = 25, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ -\frac{2 F\left (\sin ^{-1}\left (\frac{\sqrt{6-x}}{2}\right )|\frac{4}{5}\right )}{\sqrt{5}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[(6 - x)*(-2 + x)]*Sqrt[-1 + x]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 13.0673, size = 66, normalized size = 2.64 \[ - \frac{8 \sqrt{\frac{x}{5} - \frac{1}{5}} \sqrt{- \frac{x^{2}}{16} + \frac{x}{2} - \frac{3}{4}} F\left (\operatorname{asin}{\left (\frac{\sqrt{2} \sqrt{- \frac{x}{2} + 3}}{2} \right )}\middle | \frac{4}{5}\right )}{\sqrt{x - 1} \sqrt{- x^{2} + 8 x - 12}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/((6-x)*(-2+x))**(1/2)/(-1+x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.0225956, size = 74, normalized size = 2.96 \[ \frac{i \sqrt{\frac{4}{x-6}+1} \sqrt{\frac{5}{x-6}+1} (x-6)^{3/2} F\left (i \sinh ^{-1}\left (\frac{2}{\sqrt{x-6}}\right )|\frac{5}{4}\right )}{\sqrt{-(x-6) (x-2)} \sqrt{x-1}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[(6 - x)*(-2 + x)]*Sqrt[-1 + x]),x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.025, size = 43, normalized size = 1.7 \[ -{\frac{2\,\sqrt{5}}{5}\sqrt{-2+x}\sqrt{6-x}{\it EllipticF} \left ({\frac{1}{2}\sqrt{6-x}},{\frac{2\,\sqrt{5}}{5}} \right ){\frac{1}{\sqrt{- \left ( x-6 \right ) \left ( -2+x \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/((6-x)*(-2+x))^(1/2)/(-1+x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-{\left (x - 2\right )}{\left (x - 6\right )}} \sqrt{x - 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-(x - 2)*(x - 6))*sqrt(x - 1)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{-x^{2} + 8 \, x - 12} \sqrt{x - 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-(x - 2)*(x - 6))*sqrt(x - 1)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- \left (x - 6\right ) \left (x - 2\right )} \sqrt{x - 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((6-x)*(-2+x))**(1/2)/(-1+x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{-{\left (x - 2\right )}{\left (x - 6\right )}} \sqrt{x - 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-(x - 2)*(x - 6))*sqrt(x - 1)),x, algorithm="giac")
[Out]