Amazing integrals and how is solved it

Question

There a lot of integrals, however many people solved it in different ways, we can find interesting integrals in Table of Integrals, Series, and Products. I wonder What is the most exciting integral that you solved, created or found it, if you can, also write the solution of the integral, we can find very nicely methods.

Answer 1

$$\int_{0}^{1} \frac{\ln(x^2+1)}{x^2+1}$$ I really like this. It seems to be posted again and again. Solutions can be found here: Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$