I want to calculate Fourier transform of $K(x)=\log \left|\frac{1+x}{x}\right|$, the result is $\widehat{K}(\xi)=c \frac{e^{2 \pi i \xi_{-1}}}{|\xi|}$, where $c$ is some complex constant.
Editted: I searched the Math.SE again, it is similar to Fourier transform of $\log |x|$. $\log \left|\frac{1+x}{x}\right|=\log|x+1|-\log|x|$, thus I can get the result. I do not want to delete this question, you can share other ways to solve this question. Thanks!
