# Primitive of Exponential Function/Complex

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## 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.

$\blacksquare$

## Sources

- For a video presentation of the contents of this page, visit the Khan Academy.