I'm trying to prove that the following contour integral approaches 0 as R -> $\infty$. How exactly would we go about doing this?  \int{\log\left(z^{2} + 1\right) \over 1 + z^{2}}\,{\rm d}z\quad \...
### How to evaluate $\int_{0}^{\infty} \frac{\log(x^{2}+1)}{x^{2}+1}$ [duplicate]
I tried to find $f(a) = \int_{0}^{\infty} \frac{\log(x^{2}+a^{2})}{x^{2}+b^{2}}$. After differentiating I get : $f(a) = \frac{\pi \log(a+b)}{b} + C$. But it's not easy to find this constant. I ...