Branch cut for integral of (log x)^4/(1+x^2) from 0 to infinity

[logmarie]

Homework Statement

Define the branch cut prior to solving the following:
integrate from 0 to infinity of [log x]^4/ [1+x^2]

Homework Equations

The only poles inside the upper half plane is i

The Attempt at a Solution

How do I separate the countour?---help.

Thanks.

 

[Dick]

Just put a branch cut along the negative real axis. Now integrate along the real axis avoiding the singularity at z=0 with a little arc and closing in a big arc. I think you need to work out the lower powers of log(x) before you go direct to log(x)^4, but there may be a trick.