# How do you integrate f(x) = e^-|13x|?

#### Explanation:

Given function:

$f \left(x\right) = {e}^{- | 13 x |}$

1) If $x < 0$ $\setminus \implies f \left(x\right) = {e}^{13 x}$

$\setminus \setminus \int f \left(x\right) \setminus \mathrm{dx}$

$= \setminus \int {e}^{13 x} \setminus \mathrm{dx} = \frac{1}{13} {e}^{13 x} + C$

1) If $x \ge 0$ $\setminus \implies f \left(x\right) = {e}^{- 13 x}$

$\setminus \setminus \int f \left(x\right) \setminus \mathrm{dx}$

$= \setminus \int {e}^{- 13 x} \setminus \mathrm{dx} = - \frac{1}{13} {e}^{- 13 x} + C$