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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.

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