# Integration of Constant of Power X

The integration of any constant of power $x$ is important and belongs to the exponential formulae. It is one of the simplest formulas of integration.

The integration of constant of power x is of the form

Where $a$ is any constant and must not be 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, the integral sign $\int {}$ and $\frac{d}{{dx}}$ on the right side will cancel each other out, i.e.

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

We have integral

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