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Integrate doesn't yield what I expect

• To: mathgroup at smc.vnet.net
• Subject: [mg25373] Integrate doesn't yield what I expect
• From: "Borut L" <justmyname at email.si>
• Date: Sun, 24 Sep 2000 16:29:07 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Helo,

I am integrating a function which has the form
1/(x Sqrt[a x^2+b x+c]),
where c<0 and delta=4 a c-b^2 <0.
Matematica always returns same result (with Log, the one with delta>0),
despite giving option Assumptions->{...}. I expect a result with ArcSin. Is
there other way to treat such somplex integrals?

In my real assignemt I have an integral 1/(x^2 (a x^2+b x+c)^(3/2)) with
same c and delta. I expect again something with ArcSin or ArcCos, but the
Log is again yilded.

Can you also guide me to the best book with solved integrals? (best means
number of integrals solved)

Thanks, Borut