To find the integral of the function \(\int \frac{1}{x + \sqrt{x - 1}} \, dx\), let's proceed with the following steps:

### Step 1: Substitution
Let us use the substitution:
\[
u = \sqrt{x - 1}
\]
This implies:
\[
u^2 = x - 1 \quad \Rightarrow \quad x = u^2 + 1
\]
Differentiating both sides with respect to \(x\):
\[
\frac{du}{dx} = \frac{1}{2\sqrt

Learn how to integrate the function 1/(x + sqrt(x - 1)) step-by-step. This problem involves using substitution method and understanding the integration of square root functions. Suitable for college-level students.

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