Question

Evaluate the integral
(in comments)

Answer 1

\[\int\limits \frac{ 1 }{ x^2 (x^2-4)^{1/2} }dx\]

Answer 2

I did a trig sub for x=2sec(theta)

Answer 3

\[\int\limits \frac{ 2\tan \theta \sec \theta }{ (2\sec \theta)^2\sqrt(4\sec^2 \theta -4) } d \theta\]

Answer 4

That is correct
Just break down the expression into sine and cosine terms. It'll be greatly simplified.

Answer 5

So i get it down to \[\int\limits \frac{ 1 }{ 4\sec \theta } d \theta\] is that correct?

Answer 6

That is absolutely correct.

Answer 7

\[\frac{ \sin \theta }{4 }\] is what i get, but how do i get it in terms of x

Answer 8

sec(theta) = x/2
cos(theta) = 2/x
Use this : sin(theta) = sqrt(1- cos^2 (theta))
You can find value of sin(theta) in terms of x from here.

Answer 9

\[\frac{ \sqrt{x^2-4} }{ 4x }+C\]