Primitive of Exponential Function/Real

From ProofWiki
Jump to navigation Jump to search

Theorem

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

where $C$ is an arbitrary constant.


Proof for Real Numbers

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

\(\ds \map {\dfrac \d {\d x} } {e^x}\) \(=\) \(\ds e^x\) Derivative of Exponential Function

The result follows by the definition of the primitive.

$\blacksquare$


Sources