Indefinite integration problem on ArcTanh(f(Cos))

*To*: mathgroup at smc.vnet.net*Subject*: [mg69933] Indefinite integration problem on ArcTanh(f(Cos))*From*: "ANDREW PALFREYMAN" <andrew_ppp at hotmail.com>*Date*: Wed, 27 Sep 2006 06:06:26 -0400 (EDT)

Hi. I'm integrating Sin[t] / (1 + k Cos[2t]) , over 0 < k < 1, using Mathematica 4.1. I'm plotting spot values k=0.1, 0.8, 0.95 over 0 < t < 10. This represents the acceleration of a charged particle in an alternating electric field, where k represents a particular modulation of its effective inertia. Although the velocity plots (the integral dt) look fine (symmetrical about zero), the plots for position (integrating velocity dt) are clearly wrong; I get a massive expression (about 20 lines!) which will not differentiate successfully back to the original velocity expression, and they are decidedly asymmetrical about zero. The position plot ought to look like a sinewave as k->0, but there's no resemblance. Andrew Palfreyman