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Re: Can't integrate sqrt(a+b*cos(t)+c*cos(2t))

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90776] Re: Can't integrate sqrt(a+b*cos(t)+c*cos(2t))
  • From: Alois Steindl <Alois.Steindl at tuwien.ac.at>
  • Date: Thu, 24 Jul 2008 04:50:53 -0400 (EDT)
  • References: <g6710s$sb6$1@smc.vnet.net>

Hello,
If I ask Mathematica 6.0.2.1 to 
Integrate[Simplify[Sqrt[5 - 4*Cos[t] + Cos[2*t]]], {t, 0, Pi}]
it gives me
1/5 Sqrt[
 2 + 4 I] (-5 I EllipticE[-(3/5) - (4 I)/5] + (2 + I) Sqrt[5]
     EllipticE[-(3/5) + (4 I)/5] - (12 - 4 I) EllipticK[-(3/5) - (
      4 I)/5] + (6 - 2 I) Sqrt[5] EllipticK[8/5 - (4 I)/5] + 
   4 I Sqrt[5]
     EllipticPi[
     1/5 + (2 I)/5, -(3/5) + (4 I)/5] + (8 + 4 I) EllipticPi[
     1 - 2 I, -(3/5) - (4 I)/5])
Taking N[%] gives
6.72288+ 6.52169*10^-15 I

I am wondering, why the Simplify helps, because
Simplify[Sqrt[5 - 4*Cos[t] + Cos[2*t]]]
just returns
Sqrt[5 - 4 Cos[t] + Cos[2 t]].

Best wishes
Alois

-- 
Alois Steindl,                           Tel.: +43 (1) 58801 / 32558      
Inst. for Mechanics and Mechatronics     Fax.: +43 (1) 58801 / 32598
Vienna University of Technology,         A-1040 Wiedner Hauptstr. 8-10   


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