Strange results

• To: mathgroup at smc.vnet.net
• Subject: [mg15389] Strange results
• From: "Ing. Alessandro Toscano Dr." <toscano at ieee.org>
• Date: Tue, 12 Jan 1999 03:14:52 -0500
• Sender: owner-wri-mathgroup at wolfram.com

The following in/out does not make sense to me:

In[2]:=
p=Integrate[Cos[x]^n,x]
Out[2]=
\!\(\(-\(\(Cos[x]\^\(1 + n\)\
Hypergeometric2F1[\(1 + n\)\/2, 1\/2, \(3 + n\)\/2,
Cos[x]\^2]\
Sin[x]\)\/\(\((1 + n)\)\ \ at Sin[x]\^2\)\)\)\) In[4]:=
p//.n->0//PowerExpand
Out[4]=
-ArcSin[Cos[x]]

In[7]:=
p//.n->1//Simplify//PowerExpand
Out[7]=
-1+Sin[x]

Isn't it true that (Integrate[Cos[x]^0,x] == x? Isn't it true that
(Integrate[Cos[x]^1,x] == Sin[x]?

Why do I get this strange result?

I am using Mathematica 3.01 on Pcs.

Thanks for any info.

***********************************
Ing. Alessandro Toscano Dr.

Universite di Roma Tre
Dip. Ingegneria Elettronica
Via della Vasca Navale, 84
00146, Roma, ITALIA

Tel. +39-6-55177095
Fax  +39-6-5579078
mailto:toscano at ieee.org
<http://ato.ele.uniroma3.it>

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