# How do you evaluate the integral inte^(-x) dx?

Aug 20, 2014

The answer is $I = - {e}^{- x} + C$.

This integral can be solved by a substitution:

$u = - x$
$\mathrm{du} = - \mathrm{dx}$
$- \mathrm{du} = \mathrm{dx}$

So, now we can substitute:

$\int {e}^{- x} \mathrm{dx} = \int {e}^{u} \left(- \mathrm{du}\right)$
$= - \int {e}^{u} \mathrm{du}$
$= - {e}^{u} + C$

and substitute back:
$= - {e}^{- x} + C$

For simple looking integrands, you should try a quick check to see if substitution works before trying harder integration methods.