I'm looking for a function which has two simple poles, and whose integral along the positive real axis from 0 to infinity is equal to its integral along the positive imaginary axis. I don't really know where to start. I'm looking at functions which have symmetry with respect to real/imaginary axes, i.e. if x is real, then f(x) = f(ix), which led me to consider things like f(z) = 1/(z^4) or f(z) = 1/(z^5), but those don't have simple poles and their integrals from 0 to infinity on the axes don't exist since they blow up at the origin. Any help is appreciated!