# Tricky integral

• Feb 4th 2009, 08:11 AM
Kaitosan
Tricky integral
{ 4/[x sqrt(x^2 - 4)] dx

The answer is 2 arcsec (x/2) but can anyone show me the steps to in solving it? I tried partial decomposition and some trig substitution but nothing really worked.
• Feb 4th 2009, 09:00 AM
Jester
Quote:

Originally Posted by Kaitosan
{ 4/[x sqrt(x^2 - 4)] dx

The answer is 2 arcsec (x/2) but can anyone show me the steps to in solving it? I tried partial decomposition and some trig substitution but nothing really worked.

Let $x = 2 \sec \theta$ so $dx = 2 \sec \theta \tan \theta d \theta$

and the integral becomes

$\int \frac{4 \cdot 2 \sec \theta \tan \theta }{2 \sec \theta \;2 \tan \theta} d \theta = 2 \int d \theta$