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How to integrate x^2/(1-x)

  1. Jun 25, 2010 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    I know I should use some kind of substitute but ... may t=1-x but what next ?

    any help will be helpfull
    thanks dimitry
  2. jcsd
  3. Jun 25, 2010 #2
    using t=1-x replace x in your integrand with x = 1-t. Also dx is replaced.

    Find dt as a function of dx.
  4. Jun 25, 2010 #3
    ok ... but can I use the same technic when I have:


  5. Jun 25, 2010 #4


    User Avatar
    Homework Helper

    You can rewrite the problem as

    (x^2 - 4 + 4)/(x+2)

    = (x^2 - 4 )/(x+2) + 4/(x+2)

    Now simplify and find the integration.
  6. Jun 25, 2010 #5
    thanks a lot !!!
  7. Jun 25, 2010 #6
    if the degree of the polynomial in the nominator is equal or higher the the degree of the polynomial in the denominator the you have to do polynomial long division to turn the expression to a whole part plus a rational quotient (a fraction with a polynomial in the nominator of a lesser degree then the polynomial in the denominator).
  8. Jun 25, 2010 #7
    Another idea:



  9. Jun 25, 2010 #8


    Staff: Mentor

    IMO, this is the simplest approach of those presented here.
    x^2/(1 - x) = -x^2/(x -1) = -x - 1 - 1/(x - 1).
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