{ 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 $\displaystyle x = 2 \sec \theta$ so $\displaystyle dx = 2 \sec \theta \tan \theta d \theta$
and the integral becomes
$\displaystyle \int \frac{4 \cdot 2 \sec \theta \tan \theta }{2 \sec \theta \;2 \tan \theta} d \theta = 2 \int d \theta $
integrate and use your substitution to get your answer