Evaluating $\int_0^\infty \frac{1}{x+1-u}\cdot \frac{\mathrm{d}x}{\log^2 x+\pi^2}$ using real methods.

Question

By reading a german wikipedia (see here) about integrals, i stumpled upon this entry

27 1.5 $$ \color{black}{ \int_0^\infty \frac{1}{x+1-u}\cdot \frac{\mathrm{d}x}{\log^2 x+\pi^2} =\frac{1}{u}+\frac{1}{\log(1-u)}\,, \qquad u \in (0,1)} $$

(Click for the source) Where the result was proven using complex analysis. Is there any method to show the equality using real methods? Any help will be appreciated =)