I was playing around with glasser's master theorem and integrals of the form $$\int\_{-\infty}^\infty \frac{1}{x^n+1}dx$$ I observed that for positive, even values of n, the solution to the integral followed the form $$\frac{\pi}{\frac{n}{2}\sin(\frac{\pi}{n})}$$, the obvious example being at n = 2, the integral equals $\pi$. I've yet to prove this pattern, but I recognized it after some fiddling around. Is this integral part of some larger concept that is already documented? For example, the way that $\int\_0^\infty \frac{x^{p-1}}{e^x-1}dx = \zeta(p)\Gamma(p), p>1$, I can't help but think about why the general solution for even values has a sine function in it.