I've seen in some answers in Brilliant.org to some very complicated limits and integrals that uses probabilistic arguments (Let $X$ be a random variable from $[0,1]$... some examples are in those answers, see also this for an example that has to do with evaluation of limit of a series) or some uses Laplace transforms or even Fourier series (Example see some answers by user Tunk-Fey: 1, 2 ). I would like to ask about a book that discusses those techniques, i.e. where to learn them?
$\bullet$ Edit: There's no problem if those techniques can only be learned from a particular section of one book or more (or even just a paper, as long as it is accessible to an upper-undergrad.).
Thanks in advance, that would really help me unlock my box of tools.