Why is this integral hard for mathematica?

*To*: mathgroup at smc.vnet.net*Subject*: [mg92672] Why is this integral hard for mathematica?*From*: Kristian Schmidt <kristian at kreutz.us>*Date*: Fri, 10 Oct 2008 04:33:56 -0400 (EDT)

Hello Consider this indefinite integral: Integrate[Sqrt[ 4 k (1 + \[Alpha] (-1 + \[Epsilon])) + (h + \[Epsilon] - h \[Epsilon])^2], \[Epsilon]] This evaluates fine. Now try the same integral with limits of 1/2 and 3/2: Integrate[Sqrt[ 4 k (1 + \[Alpha] (-1 + \[Epsilon])) + (h + \[Epsilon] - h \[Epsilon])^2], {\[Epsilon], 1/2, 3/2}] This hangs, and I haven't been patient enough to wait it out yet :) k and alpha are just real numbers, and 0<= h <= 1. Adding these assumptions didn't seem to help though. I cannot see why it hangs. If mathematica is able to compute the antiderivative just fine, isn't it just a matter of substracting the antiderivative with itself in the two limits?