# Integral of e Power X

The integration of $e^x$ is another important formula of integral calculus. This integral belongs to the exponential formulae and is one of the simplest formula of integration.

The integration of e power x is of the form

Now consider

Using the derivative formula $\frac{d}{{dx}}{e^x} = {e^x}$, 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 $\int {\left( {{e^x} + x} \right)dx}$ with respect to $x$

We have integral

Using integration of e power x, we have