simple question about direct integration

Tuneman

if I have a equation like this








I know I can integrate so that







but this does not make sense to me because I could think of many U's that if you were to take the derivitive with respect to the squiggly varibale, still includes both variables

Hurkyl

If the derivative with respect to xi includes both variables, then how does it look when you differentiate with respect to both xi and to eta?

Tuneman