Complex Analysis: Integral of x^(n-2)/(x^n+1) using Contour Integration

Today, we using complex analysis to evaluate the integral of 0 to infinity of x^(n-2)/(x^n+1). Note that our "n" can be any real number so long as it is greater than or equal to 2. Otherwise we would have a negative power on the numerator and the integral would diverge!