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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?