I have a little mathematics background so I am trying to educate myself here more thorough and comprehensive.

“Tell me, and I will forget. Show me and I may remember. Involve me, and I will understand.”

“It does not matter how slowly you go as long as you do not stop.”

Confucius

List of my favorite answers on Mathematics StackExchange:

1. A simple way to evaluate $\displaystyle\int_0^{2\pi}e^{\cos\theta}\cos(\sin\theta)\;d\theta$.
2. Easiest way to find $\displaystyle\Re\int_{0}^{\pi/2} e^{\Large e^{i\theta}}\;d\theta$.
3. Prove $\displaystyle\int_0^\infty \frac{\ln \tan^2 ax}{1+x^2}\;dx = \pi\ln(\tanh a)$.
4. Other challenging logarithmic integral $\displaystyle\int_0^1 \frac{\log^2(x)\log(1-x)\log(1+x)}{x}dx$
5. Evaluating this integral using the gamma function