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Improper Integrals, Specifically integration part

  1. Apr 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the antiderivative of (x*arctan(x))/(1+x^2)^2)


    3. The attempt at a solution

    I've had a few attempt at this (I've been working on it an embarrassingly long time) but i felt most on track doing it by parts. Here's how i went

    u = arctan(x)
    du = 1/(1+x^2)*dx

    dv = x/(1+x^2)^2
    let m = 1+x^2
    dm = 2x*dv
    v = 1/2*S(1/m^2)*dm
    subbing values back in
    v = (-1/6)*(1+x^2)^(-3)

    placing it all in uv-S(v*du)

    (1/6)*arctan(x)*(1+x^2)^(-3)-(1/6)*S(1/(1+x^2)^(4)*dx)

    Is it possible to integrate S(1/(1+x^2)^(4)*dx) easily? I thought you needed an x somewhere on top to do it by partial fractions. If no one has the time to answer this thanks anyway.
     
  2. jcsd
  3. Apr 18, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, you do not "need an x somewhere on top".
     
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