I don't know if this is something you can help with, but I am looking for some background information on integration by parts. Was the original idea different from today's? How was it first discovered? Who first discovered it? How did it change the way the world viewed calculus? Which came first, definite integrals or indefinite integrals?
The info that I have found about integration by parts is that it was derived from the product rule of differentiation, but I am not sure how... and that is really all that I can find about the topic. This is something that I would really like to incorporate into a research project, so if anyone can help out, I would really appreciate it.