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

Explanation

To solve the integral \( \int \frac{x^4}{(x-1)(x^2+1)} \, dx \), we will use the method of partial fractions and then integrate the resulting expressions.

### Step 1: Set up the partial fraction decomposition
We start by expressing \( \frac{1}{(x-1)(x^2+1)} \) in terms of partial fractions:
\[ \frac{1}{(x-1)(x^2+1)} = \frac{A}{x-1} + \frac{Bx + C}{x^2 + 1} \]
where \( A \), \( B \), and \( C \) are constants to be determined.
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