Primitive of Exponential Function/Complex

Theorem

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

where $C$ is an arbitrary constant.

Proof for Complex Numbers

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

\(\ds \map {D_z} {e^z}\)

\(=\)

\(\ds e^z\)

Definition of Complex Exponential Function

The result follows by the definition of the primitive.

$\blacksquare$

Sources

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