We recall six different analytical methods, namely extended Prelle–Singer procedure, Lie point symmetries, $\lambda$-symmetries, adjoint symmetries, Jacobi last multiplier and Darboux polynomial methods which are used to identify integrability quantifiers of nonlinear ordinary differential equations (ODEs).We point out how these methods are interconnected in the case of two-coupled first-order nonlinear ODEs.We demonstrate the interconnections with an example.