# Indefinite Integration of *a*^{x}

How to solve the indefinite integration of *a*^{x} problems: formula, example, and its solution.

## Formula

∫ *a*^{x} *dx* = (1/ln *a*)⋅*a*^{x} + *C*

This is true because

[(1/ln *a*)⋅*a*^{x} + *C*]' = (ln *a* / ln *a*)⋅*a*^{x}

= *a*^{x}.

Derivative of *a*^{x}

## Example

∫ 6^{x} *dx* = (1/ln 6)⋅6^{x}

∫ 2^{x} *dx* = (1/ln 2)⋅2^{x}

So (given) = (1/ln 6)⋅6^{x} + (1/ln 2)⋅2^{x} + *C*.