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Homework Help: Indefinite integral with a rational function

  1. Aug 7, 2012 #1
    EDIT: Problem found. This thread can now be ignored.

    1. The problem statement, all variables and given/known data

    Find the indefinite integral.

    2. Relevant equations

    ((y^2-1)/y)^2 dy

    3. The attempt at a solution

    I've attempted a few things. I first attempted to split the statement inside the outer parentheses into two fractions;

    (y^2/y - 1/y)^2 dy

    Then to reduce it to,

    (y - 1/y)^2 dy

    And then foil it and take an antiderivative. This comes out to

    Foiled: y^2 - 2 + 1/y^2 dy

    And then the antiderivative:

    y^3/3 - 2y + 1/y + C

    But I appear to still be incorrect. According to Wolfram's integral calculator, the solution is

    y^3/3 - 2y - 1/y

    I'm close. I'm apparently missing a sign somewhere, and I can't seem to find where it is, and I don't feel comfortable plugging in the answer until I know how I got there.
    Last edited: Aug 7, 2012
  2. jcsd
  3. Aug 7, 2012 #2


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    Homework Helper
    Gold Member

    Your error is just when you are finding the anti-derivative of the last term:

    [tex]\int \frac{1}{y^2}dy=-\frac{1}{y}+C[/tex]
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