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MathGroup Archive 2006

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Re: simplify a trig expression

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65432] Re: simplify a trig expression
  • From: Roland Franzius <roland.franzius at uos.de>
  • Date: Sat, 1 Apr 2006 05:38:50 -0500 (EST)
  • Organization: Universitaet Hannover
  • References: <e0j3a1$foe$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Murray Eisenberg schrieb:
> A direct substitution (with paper and pencil) gives that the integral of 
>   Cos[x]/(Sin[x] + 1) is Log[Sin[x] + 1].  This is valid provided Sin[x] 
> is not -1.
> 
> Mathematica gives:
> 
>    Integrate[Cos[x]/(Sin[x] + 1), x]
> 2 Log[Cos[x/2] + Sin[x/2]]
> 
> Is there some simple way to coerce the latter Mathematica-supplied 
> result into the paper-and-pencil answer?

In[]
Integrate[Cos[x]/(Sin[x] + 1), x] //
Times[#, 1/2] & //
Map[Power[#, 2] &, #] & //
FullSimplify

Out[]
Log[1 + Sin[x]]


-- 

Roland Franzius


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