Integral of ax
How to solve the given integral by using the integral of ax: formula, 1 example, and its solution.
Formula
Formula
The derivative of [1/(ln a)]⋅ax is
[1/(ln a)]⋅[ax (ln a)] = ax.
derivative of ax
And integral and derivative
are the opposite operations.
So the integral of ax is
[1/(ln a)]ax + C.
Example
Example
Solution
2x(3x - 1) = 6x - 2x
The integral of 6x is
[1/(ln 6)]⋅6x.
Write the coefficient -.
The integral of 2x is
[1/(ln 2)]⋅2x.
The given integral is an indefinite integral.
So write +C.
So [1/(ln 6)]⋅6x - [1/(ln 2)]⋅2x + C is the answer.