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Will Integrate[] ever finish?

• To: mathgroup at smc.vnet.net
• Subject: [mg23622] Will Integrate[] ever finish?
• From: Robert Terwilliger <raterwil at ucla.edu>
• Date: Wed, 24 May 2000 02:16:23 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I don't know if Integrate will solve my function.  The most general form is

Integrate[1/(1+a*x+b*Sqrt[c-x^2])^(3/2),x]

It has been running for over a day and I don't know if it will ever resolve.
Is it possible that Integrate will go into some infinite loop and never
stop, or will it always return my original function EVENTUALLY if it is not
symbolically integrable?