# Math Help - Completing this integration

1. ## Completing this integration

First I started out with

$
\int \sqrt{x^2 - 4} dx
$

and I used $x = 2sec\theta$

where I am now is
$
4\int \frac{sin^2\theta}{cos^3\theta} d\theta
$

how do I complete this?

2. Originally Posted by larryboi7
First I started out with

$
\int \sqrt{x^2 - 4} dx
$

and I used $x = 2sec\theta$

where I am now is
$
4\int \frac{sin^2\theta}{cos^3\theta} d\theta
$

how do I complete this?
You have $4\int \frac{\sin^2\theta}{(1 - \sin^2 \theta) \cos \theta} \, d\theta$. Now make the substitution $u = \sin \theta$.

3. See attachment

no point in converting to sines and cosines as sin^2(t) =1-cos^2(t)

and you end up with sec^3(t) -sec(t) anyway