1. The problem statement, all variables and given/known data Find the solution of the following integral 2. Relevant equations 3. The attempt at a solution I applied the above relations getting that Then I was able to factor the function inside the integral getting that From here I should be able to get a solution by simply finding the poles of the function that are inside the bounds of this integral (in this case the unit circle), using that poles to find a residue, and then summing the residue's and multiplying them by 2πi. In this case, I see four poles that are "inside" the unit circle: z= -1, z = -1/3 , z = 0, and z = 1. z= - 3 is outside of the unit circle. However, when I do this, I get a solution of -8π/9, when I know that the solution should be 2π/9. In fact, the residue of 0 comes back as undefined, and -1 , 1 as zero. Clearly I have done something wrong, though I am not sure what exactly.