0
$\begingroup$

Possible Duplicate:
Is there an easier method to this integration problem?

I am trying to solve this problem: $\int \ln \sqrt{x^2-4}dx \quad$W|A Link

I was able to break it up using log rules to this: $\frac{1}{2} \left( \int \ln{(x+2)} dx + \int \ln{(x-2)} dx \right) \quad$W|A Link

In the second form I am able to just do 2 by-parts integration's. After doing all the work and plugging in the solutions to the by parts integration's back into the second form to get a final answer of: $\frac{1}{2} \left( (x+2)(\ln (x+2) - 1) + (x-2)(\ln (x-2) - 1) \right) \quad$W|A Link

Since W|A's answers are always throughly simplified and what not I am not 100% sure whether my final answer is correct, could anyone help me confirm it?

  • 0
    Note that the W|A answer is rather inconvenient, as it includes a constant of $\pm\pi \mathrm i$ in the region $|x|\ge2$ where the integrand is real.2011-07-27

1 Answers 1

5

HINT:

Taking a derivative will undo the integration. Take it and see if it's correct.

  • 4
    We should make a T-shirt of out this :)2011-07-27