As a calculus student many decades ago, I found disturbing the n = −1 exception when integrating a power law,

xndx={xn+1n+1+C(n1),lnx+C(n=1).
(1)

I appreciated that mathematically the caveat saved us from dividing by zero. But I found it mysterious how, only at n = −1, the result, which had been a power law like the integrand, suddenly turned into a new kind of function, lnx.

The mystery returned a few years later when, as physics students, we computed the electrostatic potential of simple sources: a point, a line, and a sheet of charge. Said another way, we computed the potential of a point source in three dimensions (the point charge), in two dimensions (the line...

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