Fraexex Collections

Hard Integrals

Recently, I've been paging through this source and have been amazed at the techniques used throughout the book. Take for example, Bernoulli's Integral:

$
int_{0}^{1} x^x dx$

This seemingly simple integral has such complexity to it; it ends up being in the form of an infinite factorial summation, of which diverges to infinity.

The question remains: How does one begin to describe processes such as this one to a calculator? And more importantly, how does one describe the applications of how & why it should be used? Regardless, I'll be looking into this more deeply, now that I'm more aware of this issue.