Some husbands try to impress their wives by lifting extremely heavy objects or other extraordinary feats of physical prowess.

That will never happen in the Quintanilla household in a million years.

But she was impressed that I broke an impasse in her research and resolved a discrepancy between Mathematica 4 and Mathematica 8 by finding the following integral by hand in less than an hour:

In this series, I’ll explore different ways of evaluating this integral.In yesterday’s post, I showed that

We now multiply the top and bottom of the integrand by . This is permissible because is defined on the interior of the interval — which is why I needed to adjust the limits of integration in the first place. I obtain

Therefore, the integral becomes

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