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.So far in this series, I’ve shown that

I now employ the substitution , so that . If , then the interval of integration does not change under this substitution, and so

On the other hand, if , then the interval of integration does not change under this substitution but the endpoints get flipped:

I can consolidate these two cases by writing

Clearly, the integral diverges if , and so I’ll ignore this special case from now on.

I’m almost done; I’ll complete the evaluation of this integral in tomorrow’s post.

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