I am searching for two kinds of books.
(1) Comprehensive books that collect, explain, and provide many examples (that is, fully worked problems) of advanced integration techniques (that is,
something at the level of difficulty of the tables written by
Gradshteyn and Ryzhik, but obviously with explanations, examples and
(2) Comprehensive books that collect, explain, and provide many examples (that is, fully worked problems) of really unusual and slick integration
techniques (which may however not be so advanced or use special
- sum of series using mean value theorem
- Deciding whether two metrics are topologically equivalent in the space $C^1()$
- Laplacian in polar coordinates
- Negation of uniform convergence
- Is there a non-compact metric space, every open cover of which has a Lebesgue number?
- Why is the Daniell integral not so popular?
Can you point out some good references?
Related question: “Really advanced techniques of integration (definite or indefinite)”.
Remark: Clearly, an answer should add some references that have not been mentioned yet (either in the comments or in the related thread),.
I think the collected works of Ron Gordon on math.stackexchange is definitely worth mentioning!!