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Calc 2 problem

  1. Mar 20, 2009 #1
    1. The problem statement, all variables and given/known data
    I am supposed to evaluate the integral using partial fractions.
    [tex]\int \frac{1}{(x+5)^2(x-1)} dx[/tex]

    2. The attempt at a solution

    So after doing all the work, I get
    [tex](-1/36)ln|x+5| - (13/6)ln|x+5| + (1/36)ln|x-1|[/tex]

    But the answer in the book appears as
    [tex](-1/36)ln|x+5| - (1/6)\frac{1}{x+5} + (1/36)ln|x-1|[/tex]

    Here is what I have before I integrate it.
    [tex]\int \frac{-1/36}{x+5} - \frac{1/6}{(x+5)^2} + \frac{1/36}{x-1} dx [/tex]
    I assume it has to do with the (x+5)2, but I can't figure out what happened to get that.
     
  2. jcsd
  3. Mar 20, 2009 #2

    Gib Z

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    Homework Helper

    Well, theres some sort of sign error involving the term we are concerned with, but disregarding that, the books answer is correct.

    What is the antiderivative of 1/x^2 ? I don't see where you pulled a log from.

    Welcome to PF btw =] !
     
  4. Mar 20, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Please show how you got that. What partial fractions did you get and how did you integrate each?
     
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