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The problem and solution can be found here: Wolfram Alpha Solution (Click show steps tab to see work)

The method Wolfram Alpha uses to solve this integral involves many many sub steps. Are there any other easier ways to solve this integral or is this the only option?

Edit: The integral to be solved is $\int \log{\sqrt{x^2-4}}\,dx.$

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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 integral is real.2011-07-27

1 Answers 1

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$\log\sqrt{x^2-4}=(1/2)\log(x^2-4),\qquad \log(x^2-4)=\log(x+2)+\log(x-2)$

Now use integration by parts to do the two integrals that result.

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    Yes, that's right.2011-07-27