How to solve the following integral using residue in complex analysis: $$\int\limits_{0}^{\infty}\frac{\ln{(1+y^4)}}{1+y^2}dy$$ Please give a hint. I know that we need to choose a contour in the upper half plane. But here the log term is creating some trouble
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Asked 6 hours before, may be useful https://math.stackexchange.com/questions/3661973/evaluation-of-int-0-pi-2-log-left1-cos2-2x-right-mathrmdx – popi May 07 '20 at 00:04
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I posted an answer here that avoids having to deal with branch points in the upper half-plane. – Random Variable May 08 '20 at 22:21