Partial Fraction Integration - Set up problems?

  1. 1. The problem statement, all variables and given/known data
    [tex]\int[/tex][tex]\frac{2x^{2}}{(x^{2}-1)}[/tex] dx


    2. Relevant equations
    Partial Fractions


    3. The attempt at a solution
    2[tex]\int[/tex][tex]\frac{x^{2}}{(x^{2}-1)}[/tex] dx

    2[tex]\int[/tex][tex]\frac{x^{2}}{(x-1)(x+1)}[/tex] dx

    [tex]\frac{A}{x-1}[/tex] + [tex]\frac{B}{x+1}[/tex] = [tex]\frac{x^{2}}{(x+1)(x-1)}[/tex]

    A(x+1) + B(x-1) = x[tex]^{2}[/tex]

    Solving for coefficients does not work because there is no x[tex]^{2}[/tex] term of A or B and also when solving for the x and the constant contradictory answers occur. Did I set this up wrong??
     
  2. jcsd
  3. danago

    danago 1,125
    Gold Member

    Perhaps try polynomial long divison first
     
  4. I can't believe I didn't see that; thank you!!
     
  5. danago

    danago 1,125
    Gold Member

    No problem :smile:
     
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