Indefinite Integration of ax

Indefinite Integration of a^x

How to solve the indefinite integration of ax problems: formula, example, and its solution.

Formula

(integral of a^x dx) = (1/ln a)(a^x) + C

ax dx = (1/ln a)⋅ax + C

This is true because
[(1/ln a)⋅ax + C]' = (ln a / ln a)⋅ax
= ax.

Derivative of ax

Example

Find the given indefinite integral. The integral of [2^x(3^x - 1)] dx

∫ 6x dx = (1/ln 6)⋅6x
∫ 2x dx = (1/ln 2)⋅2x

So (given) = (1/ln 6)⋅6x + (1/ln 2)⋅2x + C.