Thanks so much. I worked it out as you have laid it out and received the correct answer. but how did you know to put the contour only in the upper half plane?
1.I am trying to evaluate the \int\frac{ln(x)}{(x^{2}+1)^{2}} from 0 to inf2. I think I am having problems defining what my branch cut should be.
3. Here is what I have tried to no avail. First set the branch cut from -infty to 0. Then changing it to a contour integral gives us...