First, we can simplify the integrand by dividing each term by $x^2$:
$$\int \frac{x^{4}-1}{x^{2}} dx = \int (x^2 - \frac{1}{x^2}) dx$$
Now, we can integrate each term separately:
$$\int (x^2 - \frac{1}{x^2}) dx = \int x^2 dx - \int \frac{1}{x^2} dx$$
Recall
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