Is there a simple generic solution to the following integral

Question

I have the following integral: $$ I(k) = \int_{-\infty}^{+\infty} f(g(x)) g'(x) \exp\left(j k x\right) dx. $$

Is there a generic way to solve this integral? If not, I can start expanding the functions in the question.

Here, $j = \sqrt{-1}$.

P.S.: The expansion of these functions are genuinely daunting.