`int(dx)/(x(x^(4)-1))`

Explanation

To solve the integral \( I = \int \frac{dx}{x(x^4 - 1)} \), we will use the method of partial fractions. Let's go through the steps in detail.

### Step 1: Factor the Denominator
First, we need to factor the denominator \( x^4 - 1 \). We can factor it as follows:
\[ x^4 - 1 = (x^2 - 1)(x^2 + 1) = (x - 1)(x + 1)(x^2 + 1) \]
Thus, the integral can be rewritten as:
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