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A difficult integral

  1. Sep 3, 2007 #1
    How would one go about solving this?

    [tex]\int_{ - \infty }^\infty {{1 \over {q^2 + C/\left| q \right|}}dq}[/tex]

    Or,

    [tex]\int_0^\infty {{1 \over {q^2 + C/q}}dq} [/tex]

    With [tex]C > 0[/tex] obviously.

    I came across this in a physics problem. A solution exists (verified by Mathematica).

    Thanks,
    Chen
     
  2. jcsd
  3. Sep 3, 2007 #2

    HallsofIvy

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    Science Advisor

    Multiply both numerator and denominator by q:


    [tex]\int_0^\infty {{q \over {q^3 + C}}dq} [/tex]
    q3+ C can be factored as (q+ C1/3)(q^2- C1/3q+ C2/3) and then use partial fractions. The exact form will depend upon whether q^2- c1/3q+ C can be factored with real numbers and that will depend upon C.
     
  4. Sep 3, 2007 #3
    Cheers. I should've thought of that myself. :-)

    Chen
     
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