# Integration of Constant Power X

Integration of any constant of power $x$ is another important integral calculus; this integral belongs to exponential formulas category and is one of the simplest formula of integration.

The integration of constant of power x is of the form

Where $a$ is any constant and not must be not equal to zero.
Now consider

Using the derivative formula $\frac{d}{{dx}}{a^x} = {a^x}\ln a$, we have

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

Since integration and differentiation are reverse processes to each other , so the integral sign $\int {}$and $\frac{d}{{dx}}$ on the right side will cancel each other, i.e.

Example: Evaluate the integral $\int {\left( {{7^x} + 3{x^2}} \right)dx}$ with respect to $x$

We have integral

Using integral formula $\frac{d}{{dx}}{a^x} = {a^x}\ln a$, we have