       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

>

>

```

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