\displaystyle I = \int_{0}^{\infty} \frac{\ln{x}}{(1+x^2)^2}\;{dx} = \int_{0}^{1} \frac{\ln{x}}{(1+x^2)^2}\;{dx}+ \int_{1}^{\infty} \frac{\ln{x}}{(1+x^2)^2}\;{dx} 