Integrate $\ln(x^2+1)/(x^2+1)$

Question

How to evaluate $$\int_0^\infty \frac{\ln(x^2+1)}{x^2+1} \mathrm{d}x$$ using complex analysis?

I've spent ages trying to think of some clever contour integral which will give it, but I can't seem to get anywhere. Any hints would be appreciated.