Great books on all different types of integration techniques
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).
I wouldn't consider my book great or elementary but have a look at it
Advanced integration techniques
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).