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 represent constant as $\int_{0}^{\infty} \frac{\log(x^{2}+1)}{x^{2}+1} - \pi \log(2)$. Any hints ?
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Also: https://math.stackexchange.com/questions/358386/evaluating-int-0-infty-frac-lnx21x21dx. – Both found instantly with Approach0 – Martin R Nov 27 '17 at 08:55
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did you forget $dx$ on purpose? – T C Molenaar Nov 27 '17 at 08:57