In the integral

By Trigonometric Substitution:

so that the integral becomes

= [tex]\int\frac{a\sec^2(\theta)\,d\theta}{{a^2+a^2\tan^2 (\theta)}}[/tex]

=

=

(provided ''a'' > 0).

The long and short of it is when you have an integral of the form you get an result of the form:

It's a good one to memorize.