Primitive of Exponential Function/Real

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Theorem

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

where $C$ is an arbitrary constant.


Proof for Real Numbers

Let $x \in \R$ be a real variable.

\(\displaystyle \map {D_x} {e^x}\) \(=\) \(\displaystyle e^x\) Derivative of Exponential Function

The result follows by the definition of the primitive.

$\blacksquare$


Sources