Hi - Thanks for the good info - I'm sorry I didn't check the equation after I copied and pasted it, and I thought maybe it would display properly if cut and pasted from the post. I am using Mathematica 9 Home Edition, and the equation is (in plain letters):
Assuming[x>0&&a>0&&k>0&&m>0,FullSimplify[Integrate[(k(1+a)(1-a (t/m)^k)^(1/a)(t/m)^k)/t,{t, 0, x}]]]
I cut and pasted the above, just to be sure it survived the process, and then I quit the kernel before evaluating, and I get the answer:
ConditionalExpression[1 + E^((I [Pi])/a) (a - (m/x)^k)^(1 + 1/a) (m/x)^(-(1 + 1/a) k), (m/x)^k < a && a^(1/k) x <= m]
(copying and pasting the output looks good on my Mathematica) I'm fairly sure the Exp[i [Pi]/a] term should not be there, but what really concerns me is the condition. Since all parameters are positive, it appears to be invariably False.
To Sean Clarke - Thanks for the note on Reduce - I did not know that, and that solves some puzzles I have been dealing with. However, using Solve as you suggests gives me "Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>" and I am very interested in everything about this equation.
I don't expect anyone to obsess over the mathematical intricacies of the equation, just to see if the outputs match on other versions, or some obvious syntax problem I am having.
