Great books on all different types of integration techniques It's coming up to Christmas so I can ask to have all the books I can't afford from begrudging relatives! I'm really interested (mainly from looking at some of the answers cleo and other fantastic users!) in being able to approach integrals from a variety of different ways and learning how to tackle  non-elementary integrals. 
I've gone over a lot of the standard techniques in my undergrad and this is just for a hobby, so don't want anything too 'heavy', just great explanations and a lot of questions to tackle. So far I've found Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals. Many thanks.
 A: I wouldn't consider my book great or elementary but have a look at it
Advanced integration techniques 
A: If after three years your interest in evaluating definite integrals has not waned, you may consider consulting the following texts:


*

*Improper Riemann integrals by Ioannis M. Roussos (CRC Press, 2014).

*Solved problems: Gamma and beta functions, Legendre polynomials, Bessel functions by Orin J. Farrel and Bertram Ross (MacMillian, 1963).

*Integration for engineers and scientists by W. Squire (Elsevier, 1970).

*Integral evaluations using the gamma and beta functions and elliptical integrals in engineering: A self-study approach by C. C. Maican (International Press, 2005).

*An introduction to sequences, series, and improper integrals by O. E. Stanaitis (Holden-Day, Inc. 1967).
A: You can check out the book "Inside Interesting Integrals". The full title is
Inside Interesting Integrals: A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other Stupendously Clever, Awesomely Wicked, and Devilishly Seductive Maneuvers for Computing Nearly 200 Perplexing Definite Integrals From Physics, Engineering, and Mathematics (Plus 60 Challenge Problems with Complete, Detailed Solutions).
A: *

*This question has been asked and answered elsewhere, so check for similar threads here.  [Not meant to police the question, just FYI more answers there.]

*Joseph Edwards Integral Calculus Treatise (old enough to be out of copyright and free pdfs available) has 1000+ pages of integration techniques and problems (many from the Cambridge Tripos).

*Check out Zwillinger handbook or other handbooks of Integrals.  While not as fun as a problem list, you can learn from these books also.  Especially the ones that do more than just list formulas (like CRC tables) but give some derivation or other comments.
