Integration Question

[highlightall]

Integrate:

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


I do have the answer, but I'm trying to figure out how to obtain it. I've ran through the various methods of integration (simple substitution, by parts, quotients, etc.) and have hit a dead end. Does this involve several different techniques, or am I missing something really obvious?

 

[pka]

Since you have the answer, differentiate it and reduce it to the problem.
That should give you some idea as to how to work the ‘other way’.

 

[galactus]

Try trig substitution. Let \(\displaystyle x=2sec({\theta})\)

If you want to use u-substitution, let \(\displaystyle u=x^{2}-4,\)

\(\displaystyle x=sqrt{u+4}\). Find dx.