# What is the antiderivative of e^(4x)?

Mar 10, 2017

$\frac{1}{4} {e}^{4} x + C$

#### Explanation:

This will require a u-substitution.

$\int {e}^{4 x} \mathrm{dx}$

Let $u = 4 x$
$\mathrm{du} = 4 \mathrm{dx}$
then
$\frac{1}{4} \mathrm{du} = \mathrm{dx}$

The integral becomes:
$\frac{1}{4} \int {e}^{u} \mathrm{du}$

Recall that the antiderivative of ${e}^{x}$ is equal to ${e}^{x}$

So, $\frac{1}{4} \int {e}^{u} \mathrm{du} = \frac{1}{4} {e}^{u} = \frac{1}{4} {e}^{4 x} + C$

Never forget the constant of integration.