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Integrating by partial fraction.

  1. Oct 17, 2007 #1
    1. The problem statement, all variables and given/known data

    [tex]\int \frac{dx}{(x+1)(x^2+1)(x^3+1)}[/tex]



    3. The attempt at a solution

    I tried to solve it in 3 ways.
    1)[tex]\frac{A}{(x+1)}+\frac{B}{(x^2+1)}+\frac{C}{(x^3+1)}[/tex]

    2)[tex]\frac{A}{(x+1)}+\frac{B+Dx}{(x^2+1)}+\frac{C+Ex}{(x^3+1)}[/tex]

    3)[tex]\frac{A}{(x+1)}+\frac{B+Dx}{(x^2+1)}+\frac{C+Ex+Fx^2}{(x^3+1)}[/tex]
    But it gives me nonsense.
     
  2. jcsd
  3. Oct 17, 2007 #2

    Dick

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    (x+1) divides (x^3+1). You can write the partial fraction with just linear and quadratic denominators.
     
  4. Oct 17, 2007 #3
    Then should I solve in this way?

    [tex]\frac{A}{(x+1)}+\frac{B+Dx}{(x^2+1)}+\frac{C}{(x+1)^2}+\frac{F+Ex}{(x^2-x+1)}[/tex]
     
  5. Oct 17, 2007 #4

    Dick

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    That looks ok to me.
     
  6. Oct 17, 2007 #5
    damn this prob is gonna be long
     
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