Assume , the solution is trivial in any of the cases a = 0 or b = 0 or both a = b = 0.

So, if we can proceed by Integration by parts.

.......do this last integral by parts again

Someone please check this. I still get lost when typing out solutions with LaTex

I see others replying to the thread, so i'll hold off on answering the others. i'd only answer one though, since the last two are kind of similar