# How do you find the integral of 1/(x^2+4) ?

Oct 18, 2015

$\frac{1}{2} {\tan}^{- 1} \left(\frac{x}{2}\right) + C$

#### Explanation:

Recall the rule : $\int \frac{1}{{x}^{2} + {a}^{2}} \mathrm{dx} = \frac{1}{a} {\tan}^{- 1} \left(\frac{x}{a}\right) + C$

We may use this rule to integrate the given function as follows :

$\int \frac{1}{{x}^{2} + 4} \mathrm{dx} = \int \frac{1}{{x}^{2} + {2}^{2}} \mathrm{dx}$

$= \frac{1}{2} {\tan}^{- 1} \left(\frac{x}{2}\right) + C$