Primitive of Exponential of a x/Real

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$\ds \int e^{a x} \rd x = \frac {e^{a x} } a + C$

Proof for Real Numbers

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

\(\ds \int e^x \rd x\) \(=\) \(\ds e^x + C\) Primitive of $e^x$
\(\ds \leadsto \ \ \) \(\ds \int e^{a x} \rd x\) \(=\) \(\ds \frac 1 a \paren {e^{a x} } + C\) Primitive of Function of Constant Multiple
\(\ds \) \(=\) \(\ds \frac {e^{a x} } a + C\) simplifying