Substitute , so that . The integral is then equivalent to
In general, , so .
We want the substitution made above to be reversible, so that . This restricts to the interval , and over this interval we have , so we take the positive square root in order that .
Then the integral becomes
which can be computed in several ways. One method is to integrate by parts, taking
so that
Then with , you have and , which follows from the Pythagorean identity. So