# Integral of 1 Over Square Root of 1-x^2

In this tutorial we shall another important integration that is integral of 1 over square root of ${1-x^2}$; this integral is also using as an important formula.

The integral of 1 over square root of ${1-x^2}$ is of the form

To prove this formula, consider

Using the derivative formula $\frac{d}{{dx}}{\sin ^{ - 1}}x = \frac{1}{{\sqrt {1 - {x^2}} }}$, 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