Originally Posted by

**jameshume** Hi TKH,

Thanks for your reply. Couple of typos there I hadn't spotted in my original post so no wonder your confusion at the first satement...

$\displaystyle \int \frac{dy}{dx} dx = y + C $

Starting with the product rule

$\displaystyle \frac{d}{dx}(uv) = v\frac{du}{dx} + u\frac{dv}{dx} $

So, again I made a mistake in what I had written, kinda, in that I should have written it as above, where y = uv.

So I would expect

$\displaystyle \int \frac{d}{dx}(uv) dx = uv$

I'm happy with that bit...

What I don't really get is

$\displaystyle \int u\frac{dv}{dx} dx$ becomes $\displaystyle \int u dv$?

I had a slight realisation when writing this and realised why it couldn't become $\displaystyle uv$, but equally I don't understand the apparent cancelling of the "d" terms. I could understand this if they were $\displaystyle \delta $s and therefore could be algebraically manipulated in this way.

I'm gonna go back to have a little think, but if you have any illuminating answers in the mean time I'd love to hear them.

THanks agin,

James