Antiderivative Of Exponentials

Let's start with the derivative of \(a^x\):

\[ \frac{d}{dx} a^x = a^x \ln (a) \]

Since \(\ln a\) is a constant:

\[\frac{d}{dx} a^x = a^x \ln (a) \implies \frac{1}{\ln (a)} \frac{d}{dx} a^x = a^x = \frac{d}{dx} \frac{a^x}{\ln (a)} \]

This means that the antiderivative of \(a^x\) is \(\frac{a^x}{\ln (a)} + C\).

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