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Re: making a parameter in an integrand real

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116748] Re: making a parameter in an integrand real
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sat, 26 Feb 2011 06:06:13 -0500 (EST)

On 2/25/11 at 6:38 AM, alansbarnett at verizon.net (alan) wrote:

>How do I get mathematica to consider a parameter in an integrand to
>be real.

>Example: In[1]:Integrate[1/(Cos[x] Sqrt[Cos[x]2 - a2]), x]

>ArcTanh[(Sqrt[2] Sqrt[-a2] Sin[x])/Sqrt[1 - 2 a2 + Cos[2 x]]]/Sqrt[-
>a2]

>But I want a2>0 (a real).

Use Assuming with Integrate. That is:

In[1]:= Assuming[a2 > 0, Integrate[1/(Cos[x] Sqrt[Cos[x] 2 -
a2]), x]]

Out[1]= (2*Sqrt[(a2 - 2*Cos[x])/(a2 - 2)]*EllipticPi[2, x/2,
         -(4/(a2 - 2))])/Sqrt[2*Cos[x] - a2]



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