I have the idea of this integral when I see $$\int_{0}^{\infty }\!{\frac {\arctan \left( x \right) }{{{\rm e}^{\pi\,x}}-1}}\,{\rm d}x$$ and so I know that the closed form is $${\frac{1}{2}}-{\frac {\ln \left( 2 \right) }{2}}.$$
But really, I don't know any paper where I can evaluate for example $$\int_{0}^{\infty }\!{\frac {\ln \left( x \right) \arctan \left( x \right) }{{{\rm e}^{\pi\,x}}-1}}\,{\rm d}x.$$
In the same time, I see that Wolfram can't give a closed form.
Does someone has an idea please? Thanks