"This itself is a rather surprising result: Euler’s constant e comes out of nowhere!" Is it? There's an integral with a 1/x term[1]. How exactly is it surprisi

"This itself is a rather surprising result: Euler’s constant e comes out of nowhere!" Is it? There's an integral with a 1/x term[1]. How exactly is it surprising that logarithms start showing up? I realise integrating by hand is a pain, but surely it's a good idea to at least think about the integral expression before typing it into Wolfram Alpha. (EDIT: to clarify - the author takes integration for granted, yet is surprised when the integral evaluates to a logarithm; this makes little sense to me, integrating polynomials is the first thing they teach you) [1] 1/(1-x) is transformed into 1/y in a pretty straightforward substitution. When you do that with our actual integrals, you find yourself with 2 identical integrals, as you well should, given the symmetry. My solution was actually to look at the distribution of breaks already sorted into short & long, which means doing only one of the integrals (short sticks are 0..1/2) and divide by the range, since we're taking an average (i.e. multiply by 2).