# How do you integrate 1/x^2?

Jul 9, 2016

$\int \frac{1}{{x}^{2}} \mathrm{dx} = - \frac{1}{x} + C$

#### Explanation:

This function can be written as ${x}^{-} 2$.

To integrate such function we can use the general formula:

$\int {x}^{\alpha} = {x}^{\alpha + 1} / \left(\alpha + 1\right)$ for any rational $\alpha$

Using this formula we get:

$\int \frac{1}{{x}^{2}} \mathrm{dx} = \int {x}^{- 2} \mathrm{dx} = {x}^{-} \frac{1}{- 1} + C = - \frac{1}{x} + C$