1. The problem is to find the integral of the function $\frac{1}{x^2}$ with respect to $x$. 2. Recall the power rule for integration: $$\int x^n dx = \frac{x^{n+1}}{n+1} + C \quad \text{for } n \neq -1.$$ Here, rewrite $\frac{1}{x^2}$ as $x^{-2}$. 3. Apply the power rule with $n = -2$: $$\int x^{-2} dx = \frac{x^{-2+1}}{-2+1} + C = \frac{x^{-1}}{-1} + C = -x^{-1} + C.$$ 4. Rewrite the answer in a simpler form: $$-x^{-1} + C = -\frac{1}{x} + C.$$ 5. Therefore, the integral is: $$\int \frac{1}{x^2} dx = -\frac{1}{x} + C.$$