I've been going through "103 (almost) impossible integrals, sums and series" which is a book containing lots of interesting integrals. I saw a very intriguing definite integral that the book stated has a relation with Riemann's zeta function in the following manner: $$ \int_{0}^{1} \frac{\ln^2(x+1)}{x} dx = \frac{1}{4}\zeta(3) $$ I thought this connection's meaning would become clear when I prove it but now that I've proved the relation I still feel uncomfortable with it. It's just so out of place. So my question is, what is the intuition behind this equation? Why would zeta function have anything to do with this particular function's integral?
2026-04-14 00:10:28.1776125428
Why zeta function is related to this logarithmic function's integral?
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