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Sep 15, 2013 at 5:25 comment added Dong Wang Lev, thank you for the solution to the concrete problem. Actually this is the technical problem I encountered. But unfortunately I did not state the problem clearly (I just edited it), so The answer I would like to get is not exactly your construction. The $1/z$, $-1/z$ and $1/z^2$ singularities are for the meromorphic form, but not the corresponding integral. The corresponding integral has two logarithmic singularities and one $-1/z$ singularity, respectively. Thus I doubt if the answer is possible to be expressed by Elliptic functions in an elementary way. Thank you for your answer anyway.
Sep 14, 2013 at 11:52 history answered Lev Borisov CC BY-SA 3.0