Thread: Asymptotic expansion

Could somebody help me to see how to evaluate an integral from 0 to infinity of

(e^-t)*(1 + t/x)^-x as x goes to infinity

I know the answer is 1/2 + 1/8x - 1/32x^2 etc etc

Just not sure how to get to that point!

Thanks!

Can anyone help with this? I've tried integrating by parts and expanding the bit in the brackets using binomial expansion but it hasn't really got me anywhere