Often I have wondered about this question, but today I had a chance to recollect it and hence I am posting it here. During high-school days one generally learns Integration and I still loving doing problems on Integration. But I have never understood this idea of integration by parts. Why do we adopt the ILATE or LIATE rule to do problems and what was the reason behind thinking of such a rule?
Reference: http://en.wikipedia.org/wiki/Integration_by_parts