Integrate the functions`(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.

### Step 1: Set up the partial fraction decomposition

We want to express the integrand as a sum of simpler fractions. We can write:

\[
\frac{x^2 + x + 1}{(x + 1)^2 (x + 2)} = \frac{A}{x + 1} + \frac{B}{(x + 1)^2} + \frac{C}{x + 2}
...