Find the following integral (using partial fraction method)
`int(x^2+1)/((x-1)^2(x+3)) dx`

Explanation

To solve the integral \(\int \frac{x^2 + 1}{(x - 1)^2 (x + 3)} \, dx\) using the method of partial fractions, we will follow these steps:

### Step 1: Set up the partial fraction decomposition
We start by expressing the integrand as a sum of simpler fractions. The denominator \((x - 1)^2 (x + 3)\) suggests the following form for the partial fractions:

\[ \frac{x^2 + 1}{(x - 1)^2 (x + 3)} = \frac{A}{x - 1} + \frac{B}{(x - 1)^2} + \frac{C}{x + 3} \]
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