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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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marked as duplicate by Martin R, Arnaud D., Claude Leibovici integration Nov 27 '17 at 10:34

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