Several well known definite integrals can be found in the book Table of integrals series and products by I.S. Gradshteyn and I.M. Ryzhik. In this article, I present a few definite integrals which I could not find the this book. This work on definite integral is inspired by Ramanujan’s legendary work in definite integrals. I must say that finding beautiful integrals is definitely addictive.
Entry 1. If denotes the Catalan constant and denotes the Euler–Mascheroni constant then
Entry 2. If then
Entry 3. If then
Entry 6. If then
Entry 7. If denotes the Catalan constant then