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Intergal with use of arctan or arcsec?

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data


    [itex]\int \!{\frac {1}{x\sqrt {{x}^{2}-4}}}{dx}[/itex]


    2. Relevant equations
    [itex]\int \!{\frac {1}{u\sqrt {{u}^{2}-{a}^{2}}}}{du} = \frac{1}{a}{\it arcsec} \left( {\frac { \left| u \right| }{a}} \right) +C[/itex]


    3. The attempt at a solution

    u = x
    a = 2
    du = dx

    [itex]\frac{1}{2}\,{\it arcsec} \frac{|x|}{2} +C[/itex]


    1. The problem statement, all variables and given/known data

    Wolfgram and Maple 15 convert it to arctan on the last step and I dont understand why or the logic.

    [PLAIN]http://www3.wolframalpha.com/Calculate/MSP/MSP53619h6196934b27d8800001gci862h05328624?MSPStoreType=image/gif&s=36&w=443&h=386 [Broken]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
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