Explicit Conjugate: a feature or a bug?

*To*: mathgroup at smc.vnet.net*Subject*: [mg33882] Explicit Conjugate: a feature or a bug?*From*: Vladimir Bondarenko <vvb at mail.strace.net>*Date*: Sun, 21 Apr 2002 06:12:34 -0400 (EDT)*Reply-to*: Vladimir Bondarenko <vvb at mail.strace.net>*Sender*: owner-wri-mathgroup at wolfram.com

Let's consider, say, Version 4.1 . Mathematically, the following is alright. On the other hand, the answer *explicitly* contains Conjugate. Integrate[((1 - z)/(-1 + I*z))^(1/3), {z, 0, 1}] (-I)*Conjugate[(-1)^(1/3)] + ((1 + I)^(4/3)*Conjugate[(-1)^(1/3)]* Hypergeometric2F1[1/3, 1/3, 4/3, 1/2 - I/2])/2^(1/3) But Conjugate[(-1)^(1/3)] looks VERY simply: Conjugate[(-1)^(1/3)]// ComplexExpand -(-1)^(2/3) Thus, Integrate[((1 - z)/(-1 + I*z))^(1/3), {z, 0, 1}] is just -(-1)^(1/6) - ((-1)^(2/3)*(1 + I)^(4/3)* Hypergeometric2F1[1/3, 1/3, 4/3, 1/2 - I/2])/2^(1/3) which, as for me, looks much nicer (but, of cause, has the same value). Is it a feature or a problem? Vladimir Bondarenko (* P.S. IMHO, this IS a bug because identifying -(-1)^(2/3) is trivial. *)