Need help with an integral: Laplace Transform of a chirp

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Main Question or Discussion Point

I am trying to find the Laplace Transform of a chirp:
Essentially this requires evaluating an integral between zero and infinity of:

(exp(s*t))*sin(t^2) with respect to t where s is the parameter (Laplace space frequency).

Any help or advice or a redirect to some useful link would be much appreciated.
 

Answers and Replies

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TRICK: use Euler's formula [tex] 2sin(x)i=e^{ix}+e^{-ix} [/tex]

with [tex] \int_{0}^{\infty}dt.e^{at-st}= (s-a)^{-1} [/tex]

'a' here can be any real or complex number , hope it helps
 
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However doesn't the t^2 inside the sine function make the suggested trick invalid?
 

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