# Integral of Constant to the Power of a Function

The integration of any constant power of a function is a general formula of exponential functions, and this formula needs the derivative of the given function. This formula is important in integral calculus.

The integration of any constant power of a function is of the form

Now consider

Using the derivative formula , we have

Integrating both sides of equation (i) with respect to , we have

Since integration and differentiation are reverse processes to each other, the integral sign and on the right side will cancel each other out, i.e.

__Example__**:** Evaluate the integral with respect to

We have integral

Here implies that , so using formula, we have

Using the integration formula , we have