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:
To evaluate this last integral, I complete the square in the denominator. I first factor out of the denominator:
Next, I employ the substitution , so that . The endpoint of the integral do not change with this substitution, and so