integration - Help with finding $int_0^infty frac{arctan(x)log(x^2+1)}{x(x^2+1)}$

I am trying to evaluate $$\int_0^\infty \frac{\arctan(x)\log(x^2+1)}{x(x^2+1)}$$ I have tried differentiating under the integral sign, with different parameters, as well as contour integration, but I have not succeeded with neither of them. Wolfram Alpha gives a numerical value $\approx 0.754694$, but I suspect that there is a more exact answer.

I would be very glad to get some hints on how to solve it.