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MathGroup Archive 2000

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Re: Problem with antiderivtive of ArcSec

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24453] Re: Problem with antiderivtive of ArcSec
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Tue, 18 Jul 2000 00:58:56 -0400 (EDT)
  • Organization: University of Western Australia
  • References: <8k9j1o$fr1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <8k9j1o$fr1 at smc.vnet.net>, heathw at in-tch.com wrote:

> I am trying to integrate the following function:
> 1/(x*Sqrt[x^2-1])
> The solution should be simply:
> ArcSec[x]
> Mathmatica gives:
> -ArcTan[1/Sqrt[x^2-1]]

And the two answers differ by a constant.  Here is one way to get the 
textbook answer:

Notebook[{

Cell[CellGroupData[{
Cell[BoxData[
    \(TraditionalForm\`\[Integral]\_1\%y\( 
            1\/\(x\ \ at \(x\^2 - 1\)\)\) \[DifferentialD]x\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`If[y > 1, 
      1\/2\ \((\[Pi] - 
            2\ \(\(sin\^\(-1\)\)(1\/y)\))\), \[Integral]\_1\%y\( 
              1\/\(x\ \ at \(x\^2 - 1\)\)\) \[DifferentialD]x]\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(TraditionalForm\`FullSimplify[%, y > 1]\)], "Input"],

Cell[BoxData[
    \(TraditionalForm\`\(sec\^\(-1\)\)(y)\)], "Output"]
}, Open  ]]
}
]

Cheers,
   Paul

-- 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia                
Nedlands WA  6907                      
AUSTRALIA                             http://physics.uwa.edu.au/~paul


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