We demonstrate that quantities such as classical paths, action integrals, stability matrix, caustics, and so on, which are all required in semiclassical chemical dynamics, can be integrated very efficiently by means of a locally analytic integrator (LAI). Hulme's collocation method is improved to carry out these integrations systematically. LAI solves ordinary differential equations (ODEs) by recasting the set of ODEs into a set of nonlinear equations. Ari individual solution in each dimension is represented in terms of an analytic function of time for a short interval. We explicitly show that the local analyticity brings about distinct advantages.