Fourier Transform of $\frac{\log(x+C_1)}{(x^2-C_2)^2+C_3}$

Question

I have trouble in evaluating the Fourier transform of a $\log(x+C_1)$ product with $\frac{1}{(x^2-C_2)^2+C_3}$. Each one of the functions has a converging answer as $$FT[\log(x+C_1)]= \left[-\frac{1}{t}-\frac{1}{|t|}+i\pi\delta(t)-\gamma\delta(t)\right][\cos(C_1t)+i\sin(C_1t)]$$
Where $\gamma$ is the Euler constant and $\delta$ is the Dirac Delta function. Can anyone provide me idea to solve the problem or relevant reference which will be helpful?