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
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