Fourier-cosine transform of hyperbolic function

Could you help me please with the Fourier cosine transform with respect to x variable of the following function?

tanh[b(a^2+x^2)^1/2]cos(ax)/((a^2+x^2)^1/2)

Recall, that the Fourier cosine transform of the function f(x) defines by

int(f(x),0,infinity)

[Kevin Claytor]

Could you be more specific, what do you need help with?

Answer 1

[Walter Roberson]

If there is any solution at all, it would have to involve a transformation of variables. I tried a number of different representations of tanh() but none of them had an analytical solution for the fourier cosine transform.

Note: please edit existing questions instead of deleting them and re-posting.

[Asatur Khurshudyan]

I will keep in mind your note, thanks.

Shortly, that integral could not be determined by Matlab?

[Walter Roberson]

It could not be determined by Maple (I do not have access to the Matlab Symbolic Toolbox)

[Asatur Khurshudyan]

And what you think can it be solved by Symbolic Toolbox?

[Walter Roberson]

I would not expect so, but I cannot rule it out. There are some known cases where the MATLAB Symbolic Toolbox can integrate some things that Maple cannot, but I have only seen one such case myself, and I have seen a number of integrals that Maple can handle easily that the Symbolic Toolbox cannot.

If you do not already have the Symbolic Toolbox you could request a trial of it to test with.