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Explicit Conjugate: a feature or a bug?


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. *)




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