Hello everyone I need help with the following problem :
$ $ \begin{align*} \int_{0}^{\infty}\frac{\ln(x)}{(1+x)(x^{2}+1)}dx \end{align*} using the Residue theorem. I think that I could consider the contour integral \begin{align*} \oint_{C}\frac{\ln(z)}{(1+x)(x^{2}+1)}dz, \end{align*} But I'm struggling ..
also how can I define $\log(z)$ , thanks in advance
Could someone help me?