If you can solve this integral, you get a math *degree*.

I'm working on writing a detailed solution but this is a disguised gaussian integral where every number in the expression is replaced with a math concept that appear in upper division math courses. [R:Q] is the degree of the field extension R over Q which is infinite. mu(Q) is the Lebesgue measure of Q which is 0. The limit inside the parenthesis is a result of Sterling's approximation which evaluates to e. The first part of the exponent is the Levy-Civita symbol for an odd permutation which evaluates to -1. The exponent of x is the cardinality of the fundamental group of SO(3) (the group of rotations in 3D) which is 2 since the group is isomorphic to C_2 (because it has order 2 so that part really isn't necessary). I think it would be a fun opportunity to explore most of the undergraduate math curriculum.