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Homework Help: Integration of an inverse function

  1. Jan 8, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\int\frac{4}{x(x+3)}[/tex]

    2. Relevant equations



    3. The attempt at a solution

    I can get to s certain point and I know I need to do substitution but, everytime I try a substitution it just creates a more difficult problem.

    [tex]4\int(x^{-1}(x+3)^{-1})[/tex]

    I've tried substitution x^-1 for U and using (x+3)^-1 for dv but, none of it works. If someone could give me a gentle nudge it would be appreciated.

    Thanks
     
  2. jcsd
  3. Jan 8, 2009 #2

    gabbagabbahey

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    Homework Helper
    Gold Member

    This problem is an ideal candidate for the method of "partial fractions".

    Try decomposing [tex]\frac{1}{x(x+3)}[/tex] into the form [tex]\frac{A}{x}+\frac{B}{x+3}[/tex] where A and B are constants you need to determine.
     
  4. Jan 8, 2009 #3
    OH man so obvious. Your the man thank you so much. I havn't had a math class in over a year and now I'm taking diff eq. Bad idea you should definetly keep them all together.
     
  5. Jan 8, 2009 #4

    HallsofIvy

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    Science Advisor

    And, when talking about functions, be careful to distinguish between "reciprocal" and "inverse" functions!
     
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