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Re: making a parameter in an integrand real

• To: mathgroup at smc.vnet.net
• Subject: [mg116747] Re: making a parameter in an integrand real
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Sat, 26 Feb 2011 06:06:02 -0500 (EST)
• References: <ik84c3$n4v$1@smc.vnet.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 Assumptions or Assuming:

Assuming[a > 0,
 Integrate[1/(Cos[x] Sqrt[Cos[x]^2 - a^2]), x] // Simplify
 ]

Out= ArcTan[(Sqrt[2] a Sin[x])/Sqrt[1 - 2 a^2 + Cos[2 x]]]/a
-- 
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de