Question: Any build in function to find inverse fourier cosine transform?

I am using 17.02. I looked at this question, but I do not understand the answer.

I have a function F(w), and want to find f(t) using inverse cosine forurier transform.

Here is F(w)

F:= w-> cos(w*L)*cos(w*x)/(w^6+w^2*k);

All parameters are positive.

How can I use the answer shown above, or another function to find f(t)?

I can offcourse simply apply the definition myself, and I did:

int(F(w)*cos(w*x),w=0..infinity) assuming positive;

but the result is

So it does not converge. And I just wanted to check using a build-in function to verify. Strange than Maple does not have these in its inttrans package.





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