I am studying 'Integration' These are the questions I have been thinking of, but i still did not get it. 1.I understood the basic concept of dx and dy But I don't know what exactly does dx stand for in the definite and indefinite Integrals. [tex]\int x^3\, dx\right)[/tex] 2. I have read a proof in book about integration product [tex]y = u*v [/tex] [tex]dy = du*v + u*dv[/tex] [tex]\int\, dy\right = \int v\, du\right + \int u\, dv\right[/tex] [tex]\int u\, dv\right = uv - \int v\, du\right[/tex] I think it might be not serious enought. - Why is it without dy? I think it should be [tex]dy/dx = v*du/dx+u*dv/dx[/tex] first.