Risch's decision procedure for integration, not surprisingly,
uses a recursion on the number and type of the extensions from the
rational functions needed to represent the integrand. Although the
algorithm follows and critically depends upon the appropriate structure
of the input, as in the case of multivariate factorization, we cannot
claim that the algorithm is a natural one. In fact, the creator of
differential algebra, Ritt, committed suicide in the early 1950's,
largely, it is claimed, because few paid attention to his work. Probably
he would have received more attention had he obtained the algorithm as well.
-- Joel Moses, "Algorithms and Complexity", ed. J. F. Traub