Integration of power of some function is a general formula of exponential function and this formula need derivative of the given function and this formula has an importance in integral calculus.
The integration of e power x of 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 , so the integral sign and on the right side will cancel each other, i.e.
Example: Evaluate the integral with respect to
We have integral
Here implies that , so using formula, we have
Using integration formula , we have