# Integral of 1 Over 1 Plus x Squared

In this tutorial we shall look at another important integration, the integral of $1$ over $1$ plus $x$ squared. This integral also uses an important formula.

The integral of $\frac{1}{{1 + {x^2}}}$ is of the form

To prove this formula, consider

Using the derivative formula $\frac{d}{{dx}}{\tan ^{ - 1}}x = \frac{1}{{1 + {x^2}}}$, we have

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

As we know that by definition the integration is the inverse process of the derivative, we have

We know that the derivative of

This formula can also be written as