I need resources on intermediate integration techniques in integration. I am not looking for simple methods like trigonometry substitution/integration by parts/partial fraction.
I have completed school and wish to know more on intermediate integration techniques in an orderly manner. Techniques I am looking for may be similar to feyman trick of differentiation.
I want to achieve excellence in integration methods, but in an ordered manner. Should I study real analysis first before proceeding?
If you are looking to learn and better understand some of the various techniques that can be used to evaluate definite integrals, particularly improper integrals, following material that is reasonably well structured, the following texts can be consulted.
Improper Riemann integrals by Ioannis M. Roussos (CRC Press, 2014).
A treatise on the integral calculus (Volumes 1 & 2) by Joseph Edwards (MacMillian, 1921).
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).
Update
(Almost) Impossible Integrals, Sums, and Series by C. I. Valean (Springer, 2019).
An Introduction to the Harmonic Series and Logarithmic Integrals: For High School Students up to Researchers by Ali Shadhar Olaikhan (2021).