I think most of us have met integration problems concerning the trigonometric, polynomial, exponential, hyperbolic and power functions in the calculus courses. But many of the problems in this website which deal with numerical series as well as integration are far beyond the common curricula required in most mathematics undergraduate programs. For example, most of the times we are interested in the convergence of numerical sequences, but we often do not discuss the value of its convergence. Similarly, there many functions which are not standard, but which are frequently used to solve harder integrals.
Having said that, my question is: is there any suggestion about how we can master such advanced techniques for our own development as well as for the sake of students' knowledge enhancement?
I would be thankful for any reference on the subject.