I'm not sure how to approach this...

I don't know where to start. This is on an assignment largely based on integration by parts, but I can't figure out what to do. If I do integration by parts, I still have to integrate

so I'm not getting any closer to an answer.

Using online solving tools either gets me no answer, or something like this;

But it isn't much of a hint. Can someone point me in the right direction?