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Re: Error in basic integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg7730] Re: Error in basic integrals
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 2 Jul 1997 14:21:55 -0400 (EDT)
• Organization: University of Western Australia
• Sender: owner-wri-mathgroup at wolfram.com

Sean Ross wrote:

> I hope I have made an error, but I believe I have caught mathematica 3.0 returning
> a dead wrong answer to a basic integral.
> 
> Integrate[1/(1-x^2],x]    returns
> -1/2 Log[-1+x]+1/2 Log[1+x].
> 
> This result is equivalent to ArcCoth[x] which is DEAD WRONG.

Pardon?  Try differentiating the answer.  You will see that it is
correct.

> The correct answer is ArcTanh[x] according to CRC handbook etc.  Mathematica
> is retuning the complement to the correct answer.

What you should guess then is that ArcCoth[x] and ArcTanh[x] differ by a
constant -- which is easily verified:

	In[1]:= D[ArcCoth[x] - ArcTanh[x], x]
	Out[1]= 0

Cheers,
	Paul 

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia           
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au 
AUSTRALIA                              http://www.pd.uwa.edu.au/Paul

            God IS a weakly left-handed dice player
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