Yes, you are true. Even using contour integration we can do it upto n=3. But I am y\trying to get a generalized solution.
Anyway, thanks for your reply.
how to get the Fourier transform of (1+at^2)^-n ? n is a natural number such that (n>1) and a is any positive number.
i.e. ∫((1+at^2)^-n)*exp(-jωt)dt; limits of integration goes from -∞ to ∞