# How do you find the antiderivative of e^-x?

Nov 16, 2016

$= - {e}^{- x} + C$

#### Explanation:

Let
$\text{ }$
$u \left(x\right) = {e}^{- x}$
$\text{ }$
$\mathrm{du} \left(x\right) = - {e}^{- x} \mathrm{dx}$
$\text{ }$
$\Rightarrow - \mathrm{du} \left(x\right) = {e}^{- x} \mathrm{dx}$
$\text{ }$
$\text{ }$
$\int {e}^{- x} \mathrm{dx}$
$\text{ }$
$= \int - \mathrm{du} \left(x\right)$
$\text{ }$
$= - u \left(x\right) + C \text{ } C$ is a constant
$\text{ }$
$= - {e}^{- x} + C$