`(x)/((x-1)^(2)(x+2))`

Explanation

To solve the integral \(\int \frac{x}{(x-1)^2 (x+2)} \, dx\), we will use the method of partial fractions. Here’s a step-by-step solution:

### Step 1: Set up the partial fraction decomposition
We want to express \(\frac{x}{(x-1)^2 (x+2)}\) as a sum of simpler fractions. We assume:
\[ \frac{x}{(x-1)^2 (x+2)} = \frac{A}{x-1} + \frac{B}{(x-1)^2} + \frac{C}{x+2} \]
where \(A\), \(B\), and \(C\) are constants to be determined.
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