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 ____________________________________________________________________