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Re: making a parameter in an integrand real

• To: mathgroup at smc.vnet.net
• Subject: [mg116758] Re: making a parameter in an integrand real
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 26 Feb 2011 06:08:01 -0500 (EST)

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]

Assuming[a2 > 0, 
 Simplify[Integrate[1/(Cos[x] Sqrt[Cos[x]^2 - a2]), x]]]

ArcTan[(Sqrt[2]*Sin[x])/Sqrt[(1 - 2*a2 + Cos[2*x])/a2]]/Sqrt[a2]


Bob Hanlon

---- alan <alansbarnett at verizon.net> 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).