In my opinion the most curious integrals are the https://mathworld.wolfram.com/WatsonsTripleIntegrals.html https://mathworld.wolfram.com/WatsonsTripleIntegrals.

In my opinion the most curious integrals are the https://mathworld.wolfram.com/WatsonsTripleIntegrals.html https://mathworld.wolfram.com/WatsonsTripleIntegrals.html . „However, to obtain an entirely closed form, it is necessary to do perform some analytic wizardry (see Watson 1939 for details). The fact that a closed form exists at all for this integral is therefore rather amazing.“