Re: Indefinite integration problem on ArcTanh(f(Cos))

*To*: mathgroup at smc.vnet.net*Subject*: [mg69944] Re: Indefinite integration problem on ArcTanh(f(Cos))*From*: dh <dh at metrohm.ch>*Date*: Thu, 28 Sep 2006 06:14:40 -0400 (EDT)*References*: <efdks2$12a$1@smc.vnet.net>

Hi Andrew, your integral contains multivalued functions like PolyLog and Log and I suspect that you are having a branch cut problem. However, if you do not need an analytic result, it is much easier to do this numerically. E.g. setting k=0.8: f0=Interpolation[ Table[{t,Sin[t]/(1+0.8 Cos[2t])},{t,0,10,.1}] ]; f1= Integrate[Evaluate[f0[t]],t]; Plot[f1,{t,0,10}] f2= Integrate[f1,t]; Plot[f2,{t,0,10}] Daniel ANDREW PALFREYMAN wrote: > 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 > >