Hi - Im using Mathematica 9 Home edition and having some trouble. This is kind of a messy equation, but maybe there is something simple I am missing. The problem came about with the following equation. All parameters are positive, and I know that (1 + [Alpha]) (1 - [Alpha] (t/[Lambda])^k) must be positive for everything to be "nice", but I don't get what Mathematica is doing here:

In[87]:= Assuming[x > 0 && ? > 0 && k > 0 && ? > 0, 
 FullSimplify[
  Integrate[(
   k (1 + ?) (1 - ? (t/?)^k)^(
    1/?) (t/?)^k)/t, {t, 0, x}]]]

Out[87]= ConditionalExpression[?^-k (?^k + 
    E^((I ?)/?) (-1 + ? (x/?)^k)^(
     1/?) (x^k ? - ?^k)), (?/x)^
   k < ? && x ?^(1/k) <= ?]

Which I know is wrong, there should be no E^((I [Pi])/[Alpha]) in there. Also, the two constraints at the answer are mutually contradictory, they can never evaluate to true. Furthermore, if I set [Lambda]==1 in the assumptions, the E^((I [Pi])/[Alpha]) disappears and I get a correct answer. I think it might have to do with this:

Assuming[x > 0 && ? > 0 && k > 0 && ? > 0, Reduce[x ?^(1/k) <= ?, ?]]

During evaluation of In[101]:= Reduce::nsmet: This system cannot be solved with the methods available to Reduce. >>

I don't see what the problem is - it should be easily reduced, all parameters are positive.

Thanks for any help -