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...([[Riemann integral|Riemann integrability]], [[Lebesgue integral|Lebesgue integrability]], [[improper integral]]s etc.); ...al equations - conditions guaranteeing existence of solutions ([[Frobenius integrability condition]]

is an integer. J. Liouville (1841) proved that for other values of $ \alpha $ ...ons of these two equations can be found in quadratures. Other cases of the integrability of general Riccati equations have also been studied (see [[#References|[2]]

follows from the preservation of $ \omega $ (the Liouville theorem; the converse is not true, except in low dimensions). Accordingly, <TR><TD valign="top">[a1]</TD> <TD valign="top"> A.T. Fomenko, "Integrability and nonintegrability in geometry and mechanics" , Kluwer (1988) (Translat