How to take Laplace Transform of functions like sin(f'(t)) or sinh(f'(t)) where f'(t) is the derivative of another function with respect to time.
(p.s1 this information may not be relevant but f'(t) is L(f′(t)) = sL(f(t)) − f(0))
(p.s2 I was thinking of Taylor expansion of the trigonometric function before taking the Laplace transform, but I'm not sure if this is the proper way.)
I do not see how to get closed form in your case. But it may helpfull into you look into the most extensive transfoms tables at
Erdélyi "Tables of integral transforms:
Hi Amin
I've explored some possible paths, but I haven't found either any closed form. I enclose a file with some ideas I've followed (with no success!) but they could hopefully be some hints or suggestions to elaborate further.
Please let me know if you find some solution.
Good luck,
In such a case, I personally prefer numerical integration of the function (using Laplace integral definition) instead of analytical methods. However, the result will be numeric but not a function. I am not sure it can be useful for your case or not.
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