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:
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.