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Re: integrat trig radical


In a message dated 2/24/03 3:38:54 AM, mathefritz at schmieder-laher.de writes:


> is there any mathematical reason for mathematica, not 1st internally
> using
> Cos[x/2] = Sqrt[(1 + Cos[x])/2]
> before
> integrating Sqrt[1 + Cos[x]] ?
> It
> even refuses to answer True
> to
> Integrate[Sqrt[1 + Cos[x]],x] == 2*Sqrt[2]*Sin[x/2]
> 

Needs["Graphics`Colors`"];



Plot[{Sqrt[1 + Cos[x]], Sqrt[2]*Cos[x/2]},
 
     {x,-2Pi,2Pi}, PlotStyle->{Red,Blue}];



FullSimplify[Integrate[Sqrt[1 + Cos[x]],x] == 2*Sqrt[2]*Sin[x/2], -Pi<=x<=Pi]



True



Bob Hanlon




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