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Steps to find integral of 1/(x^2(x+1)(x-2)

  1. Sep 25, 2012 #1
    Hello all,

    Please I want to know the steps to find the integral primitive of this function:
    ∫1/[(x2)*(x+1)*(x-2)] dx.

    I know the result : 1/4 ln(x) - 1/3 ln(x+1) + 1/12 ln(x-2) + 1/2x

    The steps for normal function like 1/[x*(x+1)*(x-2)] were like : a/x + b/x+1 + c/x-2.
    My problem is that I'm confused about (x2), I see at the end like a derivative of x2.
    Also if we have x3, I mean (∫1/[(x3)*(x+1)*(x-2)] dx.) we will have like a + b + c + d + e. ==>

    -3/8 ln(x) +1/4x2 + 1/3 ln(x+1) + 1/24 ln(x-2) - 1/4x

    Thank you for any help about this primitive.
     
    Last edited: Sep 25, 2012
  2. jcsd
  3. Sep 25, 2012 #2

    dextercioby

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    Homework Helper

    (If this homework, it's wrongly placed. There's a special section on HW).

    You may want to check if the 3 factors in the common denominator are linearly independent. Then you should assume a decomposition into 3 terms, each of them having one factor of the product in the denominator and a polynomial of one degree less in the numerator of each fraction.

    So

    [tex] \frac{Ax+B}{x^2} [/tex]

    is your first fraction in the sum of 3 and its integral is trivial, once you find out who A and B are numerically.

    P.S. My name's not Kurt Lewin, there are just words attributed to him which I like and kept as a signature here. :smile:
     
    Last edited: Sep 25, 2012
  4. Sep 25, 2012 #3
    Thank you very much Mr. Kurt Lewin
     
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