Conceptual problem with integration by parts.

[dE_logics]

Why is it that whenever we encounter a question which can be solved by integration by parts, we get half the function?

I mean, suppose a differentiated f(x)g(x) yielded $${f'(x) g(x)dx + f(x)g'(x)dx}$$, then why do we get only $${f'(x) g(x)dx}$$ to extract the original function (f(x)g(x)) from?

 

[dE_logics]

Ok...let's forget about this question for now...dont answer it.