Re: Simplifying Log to ArcCos Expressions

*To*: mathgroup at smc.vnet.net*Subject*: [mg56901] Re: Simplifying Log to ArcCos Expressions*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Mon, 9 May 2005 01:46:50 -0400 (EDT)*Organization*: The University of Western Australia*References*: <d5kapv$299$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <d5kapv$299$1 at smc.vnet.net>, "David Park" <djmp at earthlink.net> wrote: > 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. (I'm > working with Version 5.0.1.) Why not do what you would do by hand? That is, change variables: [1] k is a constant. Dt[k] ^= 0; [2] Change variables r -> k/Cos[t]: (k/r^2) (1/Sqrt[1 - k^2/r^2]) Dt[r] /. r -> k/Cos[t] and simplify. Simplify[%, 0 < t < Pi/2] [3] Solve for t as a function of k and r. Solve[r Cos[t] == k, t] Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul http://InternationalMathematicaSymposium.org/IMS2005/

**Follow-Ups**:**Re: Re: Simplifying Log to ArcCos Expressions***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>