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I would like to find the inverse Laplace transform of the following function

$$F(s) = \frac{1}{(1+ab^{log(s)})^{c}}$$

Where a, b, and c are constants (need not be integers).

What I have done:

I have looked for any general method and found out that there is Mellin's inverse formula

$$f(t) = \mathcal{L}^{-1}\{F(s)\}(t) =\frac{1}{2\pi i}\displaystyle{\lim_{T \to \infty}}\int_{\gamma - iT}^{\gamma + iT} e^{st}F(s)ds$$

Please let me know whether it possible to have a solution exists for the given problem?

I don't have much idea about solving this integral. Kindly help me to find the inverse Laplace transform of the given function using Mellin's inverse formula. Is there any other analytical methods by which I find the inverse for the problem at hand?

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