Find Indefinite of root function

Question

I don't know how to find this strange integral

$\int{\sqrt{\dfrac{x-4}{x+2}}\dfrac{dx}{x+2}}$

Please help me solve this problem

Answer 1

HINT:

Set $$\sqrt{\frac{x-4}{x+2}}=t, \frac{x-4}{x+2}=t^2,t^2-1=\frac{-6}{x+2}, x+2=\frac6{1-t^2}$$