  The problem of inverting the total divergence operator is central to finding
components of a given conservation law. This might not be taxing for a
low-order conservation law of a scalar partial differential equation, but
integrable systems have conservation laws of arbitrarily high order that must
be found with the aid of computer algebra. Even low-order conservation laws of
complex systems can be hard to find and invert. This paper describes a new,
efficient approach to the inversion problem. Two main tools are developed:
partial Euler operators and partial scalings. These lead to a line integral
formula for the inversion of a total derivative and a procedure for inverting a
given total divergence concisely.
