Evaluate: `int1/((x-1)sqrt(x+2))\ dx`

Explanation

To evaluate the integral \(\int \frac{1}{(x-1)\sqrt{x+2}} \, dx\), we will follow a systematic approach using substitution.

### Step-by-Step Solution:

1. **Identify the substitution**:
We notice that \(\sqrt{x+2}\) is in the denominator. We can let \(t^2 = x + 2\). Thus, we have:
\[
x = t^2 - 2
...