Hi guys! I was doing a problem for my homework and I was doing great until the end. I got the integral correct and proved that the series converged but I'm having trouble understanding something. In the attached picture: I just need some explanation from at the point the limit is set up from t -> infinity and why they then set up another limit from s -> 0 and why for that latter portion they somehow got an e^{8}. Thanks for all your help guys!