# Primitive of Exponential Function/Complex

## Theorem

$\displaystyle \int e^x \rd x = e^x + C$

where $C$ is an arbitrary constant.

## Proof for Complex Numbers

Let $z \in \R$ be a complex variable.

 $\displaystyle D_z \left({e^z}\right)$ $=$ $\displaystyle e^z$ Definition of Complex Exponential Function

The result follows by the definition of the primitive.

$\blacksquare$