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Re: Simplifying Log to ArcCos Expressions

• To: mathgroup at smc.vnet.net
• Subject: [mg56882] Re: Simplifying Log to ArcCos Expressions
• From: "Peltio" <peltio at trilight.zone>
• Date: Mon, 9 May 2005 01:46:03 -0400 (EDT)
• References: <d5kapv$299$1@smc.vnet.net>
• Reply-to: "Peltio" <peltioNOSPAM at despammed.com.invalid>
• Sender: owner-wri-mathgroup at wolfram.com

"David Park" wrote

>Dear MathGroup,
>
>I want to integrate the following expression and get a simple answer.
>
>expr1 = (k/r^2)*(1/Sqrt[1 - k^2/r^2])
>
>The answer is actually quite simple: ArcCos[k/r] + constant. But what a lot
of work for me to get it! Perhaps someone can show a simpler path.

If I'm not mistaken, this is easily done by substitution.
http://www.math.hmc.edu/calculus/tutorials/trig_substitution/

Simplification should be done before calling Integrate, then.

cheers,
Peltio
Sometimes, the best way to use Mathematica is to not use it at all. : ]
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