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I need help with integration using partial fractions

  1. Sep 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Compute the integral:
    int ((1-x^2)/(x^3+x)) dx

    2. Relevant equations
    int ((1-x^2)/(x^3+x)) dx

    3. The attempt at a solution
    I think I should use the partial fraction method to simplify the fraction
    (1-x^2)/(x^3+x)= A/x + B/ (1+x^2)
    putting it in a polynomial form:
    x^2 (A)+x (B) + 1 (A)= 1- x^2
    and by equating the coefficients,
    A = -1
    B = 0
    However, A doesn't satisfy the constant on the LHS (+1)

    So what is the thing that I did wrong??

    Thanks in advance
  2. jcsd
  3. Sep 25, 2009 #2


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    Homework Helper

    I think you missed the quadratic part of your partial fraction decomposition, it should be

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