complex analysis - Evaluate $int_0^infty frac {(log x)^4dx}{(1+x)(1+x^2)}$

Evaluate

$$\displaystyle\int_0^\infty \frac {(\log x)^4dx}{(1+x)(1+x^2)}$$

This is a past final term exam problem of a complex analysis course at my university. I am studying for this year’s exam and I found this problem. The examiner assumes us to use residue calculus. Could you please give your valuable suggestions on how to proceed ?