Existence of the laplace transform $sin(8t^{3})$

Question

Apparently the laplace transform of $sin(8t^3)$ doesn't exist. No program lets me calculate it. I was asked if it existed in an exam and I said yes because it happens to meet all the criteria. Can anyone tell me if it exists or not?

Thanks.

Answer 1

$\displaystyle\int_0^\infty e^{-st}\sin(8t^3)\;dt$ isn't an elementary function.