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Re: Error in basic integrals

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

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

> 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


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 

            God IS a weakly left-handed dice player

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