Primitive of Exponential Function

Theorem

 * $\displaystyle \int e^x \ \mathrm d x = e^x + C$

where $C$ is an arbitrary constant.

Proof for Real Numbers
Let $x \in \R$ be a real number.

The result follows by the definition of the primitive.

Proof for Complex Numbers
Let $z \in \R$ be a complex number.

The result follows by the definition of the primitive.