Just verifying an integration by parts problem...

Hey all, just checking my work on an integration by parts problem I've been working on. It's coming out to 0, which makes my spider sense tingle a little bit about the methodology I used to get there. It may be right, or it may be one of those situations where I've been staring at it for too long and it's really something obvious. I know I could have cancelled those terms earlier, but I just left them while I was working on it. What do you guys think? Is my method at least correct, and do you get the same? Thank you very much in advance.