An introduction for integral tricks.

Question

I wonder if there's a good book or internet page introducing integral tricks? For example integration by parts, and Feynman's trick.

I'm not looking for an exercise book such as "Problems in Mathematical Analysis " by Boris Demidovich.

I hope the introduction categorizes by problem type and recommend tricks. For example wiki page on Ordinary Differential Equations has a section "summary of exact solutions" that does not only provide the solution, but also the solution method, e.g. Separation of variables, Integrating factor, etc.

Answer 1

I would submit a vote for The Handbook of Integration.

It covers both numerical and analytic integrals. Off the top of my head, it includes techniques such as u-substitution, integration by parts, integral transforms (ie. Mellin, Laplace), Frullani integrals, integrals by differentiation under the integral sign and integration by special functions.

Answer 2

There is a recent book that looks very interesting: Inside Interesting Integrals (2014). If you have access through SpringerLink, you can download it.