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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?

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    Haven't you asked this already here http://math.stackexchange.com/questions/53974 ?2011-07-27
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    "could anyone help me confirm it?" - differentiate your result and see if it gives back your original integrand.2011-07-27
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    No, This is sort of a follow up.2011-07-27
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    Please try to keep your posts self-contained. I have added tex to flush out your post. Please correct me if I was in error. I have not read your previous question, so I'm out of the loop there.2011-07-27
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    @mwmnj: Your previous post had also been edited by someone else to make it self-contained. Please try to learn from such edits so they won't be required in the future.2011-07-27
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    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

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HINT:

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

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