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

Explanation

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

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