are mathematicians still looking for new integral rules of analytic evaluation / simplification?are mathematicians still looking for new integral rules of analytic evaluation / simplification?
But why not ??are mathematicians still looking for new integral rules of analytic evaluation / simplification?
To answer your question as put is simple: NO! Many many years ago I wrote a PhD thesis in integration theory. But we were looking at a new definition or the integral itself but nothing to do with the sort of things I think you have in mind: ways (techniques) of doing integrals, ways of simplifying the evaluating integrals. What we did was per-computer revolution which literally changed the entire direction of mathematics education. I do encourage to look for a discussion group devoted to mathematics instruction and post this question there.
Ah! now you are asking about department politics. In most Universities in North America. In almost every university mathematics department to be an associate or a full professor one must have a PhD in mathematics and are expected to continue to publish original research. The activities you asked about are not considered part research in professional mathematics. Again, I encourage you to find a group of mathematics educators like NCTM and post your concerns.But why not ??