Laplace transform of sin(t²)

[tek49]

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.

 

[mhill]

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

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

'a' here can be any real or complex number , hope it helps

 

[tek49]

However doesn't the t^2 inside the sine function make the suggested trick invalid?