Step 1:
First, we can simplify the integral by dividing each term in the numerator by $x^{4}$:
$$
\int \frac{x^{5}}{x^{4}} dx + \int \frac{2x^{2}}{x^{4}} dx - \int \frac{1}{x^{4}} dx
$$
This simplifies to:
$$
\int x dx + \int \frac{2}{x^{2}} dx - \int
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