Find `int(x^2)/((x^2+1)(x^2+4)dx`

Explanation

To solve the integral \(\int \frac{x^2}{(x^2 + 1)(x^2 + 4)} \, dx\), we will use the method of partial fractions. Here’s a step-by-step solution:

### Step 1: Set Up Partial Fractions
We start by expressing the integrand in terms of partial fractions. We want to write:
\[ \frac{x^2}{(x^2 + 1)(x^2 + 4)} = \frac{A}{x^2 + 1} + \frac{B}{x^2 + 4} \]
where \(A\) and \(B\) are constants to be determined.
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