I need help with this:

1/(x((x^2-4)^1/2))

One divided by (x times the square root of x^2-4)

A buddy got it to a couple of ln's but I used trig substitution.

I let:

x=2sec(theta)

dx=2sec(theta)tan(theta) dtheta

So I'm integrating:

2sec(theta)tan(theta)/2sec(theta)*(4sec^2(theta)-4)

Which the 2sec(theta) cancels right away, the 4 under the radical comes out as a 2, and the (sec^2(theta)-1) turns into a tan^2(theta). Then I took the square root of the tan^2(theta) which then cancels with the above tan(theta).

So I'm integrating:

1/2

Which I get 1/2(theta), which I turn into (1/2)arcsec(x/2)

Is that right?