# Integral of 1 Over 1 Plus x Squared

In this tutorial we shall another important integration that is integral of $1$ over $1$ plus $x$ squared; this integral is also using as 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 integration is the inverse process of derivative, so we have

As we know that derivative of

This formula can also be written as