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

Jun 30, 2016

$\int {e}^{2 x} \mathrm{dx} = \frac{1}{2} {e}^{2 x} + c$

#### Explanation:

Let $u = 2 x$, hence $\mathrm{du} = 2 \mathrm{dx}$

Hence $\int {e}^{2 x} \mathrm{dx} = \int {e}^{u} \cdot \frac{\mathrm{du}}{2}$

= $\frac{1}{2} {e}^{u} + c$

= $\frac{1}{2} {e}^{2 x} + c$