Integration of any constant 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 any constant power 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