# How do you find the antiderivative of e^(-2x)?

Mar 2, 2015

Starting from the integral:
$\int {e}^{- 2 x} \mathrm{dx} =$

By substitution, you set $- 2 x = t$
so: $x = - \frac{t}{2}$
and $\mathrm{dx} = - \frac{1}{2} \mathrm{dt}$

The integral becomes:

$\int {e}^{t} \left(- \frac{1}{2}\right) \mathrm{dt} = - {e}^{t} / 2 + c$

going back to $x$:
$= - {e}^{- 2 x} / 2 + c$