Hi im new to this forum and was wondering if someone could help me with the following problem

use a suitable series expansion to find an asymptotic expansion as x approaches infinity for

the integral from 0 to infinity of [ exp(-x(t^2))sin(t) ]

i tried expanding the sine part and integrating term by term. i got stuck doing integrating term by term. i dont know how to do integral im not sure if i should use a different expansion?

thanks in advance