I do not believe this has a closed form. That is probably why you are having trouble.
Oh, I see, I misread. A general form may be tricky, but for
We can use parts.
Then we can put it together and get:
Now, try applying parts again. Can you do that?.
You are shooting for this when you're done:
You can factor out the e term to tidy up.
There is a pattern to these which may lead us to a general form.
See a pattern you can derive a general form from?. I think so.
For instance, one way could be
There is a start for you.