Integrate the rational functions`1/(x(x^4-1)`

Explanation

To integrate the rational function \( \frac{1}{x(x^4 - 1)} \), we will follow these steps:

### Step 1: Rewrite the Integral
We start with the integral:
\[ I = \int \frac{1}{x(x^4 - 1)} \, dx \]
We can factor \( x^4 - 1 \) as \( (x^2 - 1)(x^2 + 1) \), so we rewrite the integral:
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