# Integral of e to the Power of a Function

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

The integration of e to the power x 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 , and , so we can write it as

Using the integration formula , we have