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Homework Help: 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

    User Avatar
    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


    User Avatar
    Science Advisor

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