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.