1. The problem statement, all variables and given/known data the integral from negative infinity to positive infinity: z^4/(1 + z^8)dz 2. Relevant equations The residue theorem: <http://en.wikipedia.org/wiki/Residue_theorem>. 3. The attempt at a solution I found the 8th roots of z^8 = -1, which are e^(πiz), where z =1/8, 3/8, 5/8, 7/8, 9/8 11/8, 13/8 15/8. So the denominator is (z - z0)(z - z1)(z - z2) . . . (z - z7) and we can calculate the residue of each pole. Each pole has order 1, so the residue at each pole is just cauchy's formula at the pole. Then the integral is just the sum of the 8 residues multiplied by 2πi. This seems more complicated then it should be. Can anyone tell me if I am doing this right because something seems off. Thank you.