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Homework Help: Integration by parts with my work

  1. Feb 15, 2007 #1
    1. The problem statement, all variables and given/known data

    integrate arctan(1/x)

    2. Relevant equations



    3. The attempt at a solution

    z=arctan(1/x)
    dx=-dz(x^2-1)

    now its the integral of z(x^2-1)dz

    let u =X^2-1
    du=2x
    dv=-udu
    v=-u^2/2

    integral=(x^2-1)(-u^2/2) - int (-u^2)(2x)

    this is where i got stuck but i think im doing the z substitution incorrectly. is it even necessary to sub z?

    Thanks!
     
  2. jcsd
  3. Feb 16, 2007 #2

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    You got stuck because you're trying to integrate the term z(x^2-1)dz which has x's and z's in it!

    We want to calculate [tex]\int\tan^{-1}(1/x)dx[/tex]. Do this by parts, and take u=arctan(1/x) and dv=dx. You need to then calculate du and v, and use the usual integration by parts forumla: [tex]\int udv= uv-\int vdu[/tex]

    (Alternatively, you could note that arctan(1/x)=arccot(x) and proceed from here)
     
    Last edited: Feb 16, 2007
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