# How do I find the antiderivative of f(x)=e^(-2x)?

Feb 11, 2015

The exponential ${e}^{x}$ derived or integrated is always equal to itself. However, you must be careful with the exponent.
In this case you have $- 2$ in it so you have to take into account it.
So:
$\int {e}^{- 2 x} \mathrm{dx} = {e}^{- 2 x} / \left(- 2\right) + c$

You can check your result by deriving it so that you ought to get the original integrand.