How to solve this Fourier Transform? It would be very helpful even if you can just share your thoughts on the approach to such problems. It is fine if the answer has diracdelta (or its derivatives) and similar such "functions".
$FT(\sqrt{x^2-x\sin(x)}) = \int\limits_{-\infty}^{\infty}\sqrt{x^2-x\sin(x)} e^{-i y x} dx$
Edit: I changed the problem as per my brief exchange with Eric (in comments section). This is to retain focus on the main issue, which is approaching FT of functions raised to fractional powers (square root in my example).