1. ## du/u

Can somebody tell me what this means? dy/dx means a small change in y with respect to a small change in x. du/u means a small change in u with respect to no change in u?

2. Don't reply to this. I have worked it out. In the conext it was just a bit of algebraic manipulation.

3. It's just a shorthand way of writing the chain rule in reverse (for integration, the reverse process of differentiation).

$\int{f\left(g(x)\right)\,g'(x)\,dx} = \int{f(u)\,\frac{du}{dx}\,dx} = \int{f(u)\,du}$ by making the substitution $u = g(x)$.

In your case, $f\left(g(x)\right) = \frac{1}{g(x)}$.