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Integration by substitution

  1. Sep 27, 2011 #1
    Hi , I solved [itex]\int (1/((\sqrt{(x^2)+(a^2)}))^(3/2)*dx)[/itex] using the substitution x = a*tan([itex]\varphi[/itex] I wonder if there are other methods to solve this problem?
    * (2/3) is the power on the radical function
     
    Last edited: Sep 27, 2011
  2. jcsd
  3. Sep 27, 2011 #2
    So the problem is
    Integral ( x^2 + a^2 ) ^ (-3/4) dx ?

    Is that correct ?
     
  4. Sep 28, 2011 #3
    Integral ( x^2 + z^2 )^(-3/2)dx I'm sorry I wrote the integral wrong in the first post
     
    Last edited: Sep 28, 2011
  5. Sep 28, 2011 #4
    Attached is the solution with z=3
    Cheers
     

    Attached Files:

  6. Sep 28, 2011 #5
    Thanks paulfr but I already said that I solved it with the same substitution x=a*tan(u). I'm asking whether another method exist to solve the integral
     
  7. Sep 28, 2011 #6

    dextercioby

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    Try [itex] x=a\sinh t [/itex].
     
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