Re: simplification

*To*: mathgroup at smc.vnet.net*Subject*: [mg122193] Re: simplification*From*: dimitris <dimmechan at yahoo.com>*Date*: Thu, 20 Oct 2011 07:42:56 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <j7m5th$jo6$1@smc.vnet.net>

I would like to add some background for the expression. This expression arose when I tried to evaluate with Mathematica the following indefinite integral intMath=Integrate[1/((x^2 + x + 1)*Sqrt[x^2 - x + 1]), x] and Mathematica produced above lengthy expression. This integral appeared in another forum. What it is very interesting is that the person who mentioned the integral gave an expression for the antiderivative which is just: intUser=ArcTan[(Sqrt[2]*(1 + x))/Sqrt[1 - x + x^2]]/Sqrt[2] + ArcTanh[(Sqrt[2/3]*(-1 + x))/Sqrt[1 - x + x^2]]/Sqrt[6]; As you can see this is a correct antiderivative since D[intUser, x] - 1/((x^2 + x + 1) Sqrt[x^2 - x + 1]) // FullSimplify 0 User's antiderivative and Mathematica's differ just a single constant: Chop[Table[intUser - intMath /. x -> RandomReal[{-1000, 0}], {20}]] Chop[Table[intUser - intMath /. x -> RandomReal[{0, 1000}], {20}]] (*output omitted*) I have tried with a lot of ways to simplify Mathematica's lengthy expression, just by curiosity, trying every way I know (and I remember! It has been a lot time since I dealt with procedures like this.) But I thought it will be an interesting thread for many people in this forum! Dimitris P.S. It doesn't have a connection with my original query, but just for the record: User's antiderivative is continuous in the whole real axis. Mathematica is not.