Integrate the following functions `(x-1)/sqrt(x^2-1)`

Explanation

`(x-1)/sqrt(x^2-1) = x/sqrt(x^2-1)-1/sqrt(x^2-1)`
if we put t = `x^-1`, we have
`dt = 2x dx gt xdx = dt/2`
therefore` int x/sqrt(x^2-1) dx = int 1/sqrtt dt/2 = sqrtt = sqrt(x^2-1)`
Thus, `int (x-1)/sqrt(x^2-1) dx`
= `sqrt(x^2-1)-log|x+sqrt(x^2-1|+c`