Friday May 2

I pointed out that step 1 of the partial fractions expansion algorithm -- long division of the numerator by the denominator, leaving a remainder term -- can be thought of as "peeling off the terms that blow up at x = infinity". Which can be done almost the same way as we do the rest of the algorithm; divide by the highest power of x, then look at the limit as x->infinity.
Not that there's much reason to do it that way; I was just sayin'.

Then we did improper integrals. I spent a long time on one example: integral₀^picot(x) dx. This is improper at both ends, and there's no best way to evaluate it, in that different approaches give different answers. So one should declare this to have no answer.