I have learn the basic integration techniques: Integration by parts, partial fraction decomposition, recursion formulae, and others that would be considered in ordinary calculus courses. What amazes me on MSE is the plethora of methods to evaluate difficult integrals, may it be with Gamma or Beta functions, Frullani, different classes of integrals (elliptic, exponential etc.) and many others. I have yet to study residue calculus, neither Fourier analysis, but I would be surprised to see that these techniques would come up in those courses.
My question is if there is any literature on this matter, that covers these seemingly advanced techniques and not just the basic methods? Or is this just a matter of experience?