While going through some of my notes, I came across a formula for evaluating an integral of the form: $$\int_0^\infty {\frac{dx}{x^n+1}} = \frac{\pi}{n\sin(\frac{\pi}{n})}$$
I was wondering if any other formulas exist for solving more complicated integrals where an antiderivative can't easily be found. If you could also include a proof of said formula, that would also be greatly appreciated.
Thanks in Advance!