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

Explanation

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

### Step 1: Set up the partial fraction decomposition
We want to express the function in the form:
\[ \frac{x^2 + x + 1}{(x + 1)^2 (x + 2)} = \frac{A}{x + 1} + \frac{B}{(x + 1)^2} + \frac{C}{x + 2} \]
where \(A\), \(B\), and \(C\) are constants we need to determine.
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