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Homework Help: Misc integral

  1. Mar 29, 2010 #1
    [tex]
    \int \frac{dx}{x(x^4+1)}
    [/tex]
    [tex]
    u=x^2
    [/tex]
    [tex]
    \sqrt{u}=x
    [/tex]
    [tex]
    dx=\frac{1}{2\sqrt{u}}
    [/tex]
    [tex]
    \frac{1}{2}\int \frac{du}{u^2+1}
    [/tex]
    [tex]
    \frac{1}{2}arctanx^2+C
    [/tex]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 29, 2010 #2

    Mark44

    Staff: Mentor

    The integral above isn't right. You forgot to replace the x factor in the denominator.
     
  4. Mar 30, 2010 #3
    [tex]
    \frac{1}{2} \int \frac{du}{u(u^2+1)}=\int \frac{A}{u}+\frac{Bu+C}{u^2+1}du
    [/tex]
    [tex]
    A=\frac{1}{2}=-B
    [/tex]
    [tex]
    ln|x|-\frac{1}{4}ln(x^4+1)+C
    [/tex]
     
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