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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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marked as duplicate by J. M., t.b., mixedmath, Pete L. Clark, Asaf Karagila Jul 28 '11 at 16:14

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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Haven't you asked this already here math.stackexchange.com/questions/53974 ? –  Mariano Suárez-Alvarez Jul 27 '11 at 3:01
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"could anyone help me confirm it?" - differentiate your result and see if it gives back your original integrand. –  J. M. Jul 27 '11 at 3:01
    
No, This is sort of a follow up. –  Matt Jul 27 '11 at 3:02
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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. –  mixedmath Jul 27 '11 at 3:06
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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. –  joriki Jul 27 '11 at 3:12
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1 Answer

up vote 5 down vote accepted

HINT:

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

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4  
We should make a T-shirt of out this :) –  Mariano Suárez-Alvarez Jul 27 '11 at 4:36
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