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

Explanation

To solve the integral \(\int \frac{x-1}{\sqrt{x^2-1}} \, dx\), we can split the integrand into two separate terms:

\[ \int \frac{x-1}{\sqrt{x^2-1}} \, dx = \int \frac{x}{\sqrt{x^2-1}} \, dx - \int \frac{1}{\sqrt{x^2-1}} \, dx \]

Let’s denote these two integrals as \(I_1\) and \(I_2\):

...