find the integral of squreroot of (5-x)/(x-2)dx.please answer this question

Hi ,

∫√((5-x)/(x-2)) dx

  take , √(x-2) = y

   x = y² +2

     dx = 2y dy

 2∫√(5- y² -2)/ y *y dy =2∫√(3- y²) dy

= 2√3 ∫(1- (y/√3)² ) dy

y/√3 = sin z

dy = √3 cos z dz

= 2√3 ∫(1- sin² z ) cos z dz

= 2√3 ∫ cos ²z dz

= √3 ∫( 1+cos2z) dz

= √3 [z + sin 2z/2 ]

= √3 [sin ⁻¹( (√ (x-2)/3)  + cos (sin ⁻¹( √( (x-2)/3)) +√ ((x-2)/3) +K

Hope it helps you !