Evaluate: `int_1^3 1/(x^2(x+1))dx`

Explanation

To evaluate the integral \( \int_1^3 \frac{1}{x^2(x+1)} \, dx \), we can start by simplifying the integrand using partial fraction decomposition.

### Step 1: Partial Fraction Decomposition
We want to express \( \frac{1}{x^2(x+1)} \) in the form:
\[ \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x+1} \]
Multiplying through by the denominator \( x^2(x+1) \) gives:
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