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I Partial Fraction Decomposition With Quadratic Term

  1. Oct 1, 2016 #1
    Hey, all! I'm learning partial fraction decomposition from Serge Lang's "A First Course in Calculus." In it, he gives the following example:

    [tex]\int\frac{x+1}{(x-1)^2(x-2)}dx [/tex]

    He then decomposes this into the following sum:

    [tex] \frac{x+1}{(x-1)^2(x-2)} = \frac{c_1}{x-1}+\frac{c_2}{(x-1)^2}+\frac{c_3}{x-2} [/tex]

    My question is this: On the right hand side (RHS), ##x-1## and ##(x-1)^2## appear. Why is this the case, when the original denominator only had the ##(x-1)^2##? I hope this makes sense, and any help here is greatly appreciated!
  2. jcsd
  3. Oct 1, 2016 #2


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    If you left out the x-1 denominator term, then the numerator for [itex](x-1)^2[/itex] would be a+bx. The expression you are given is equivalent and is easier to integrate.
  4. Oct 1, 2016 #3
    I'm afraid I don't really understand. Could you explain more explicitly, or direct me to a good resource on this?
  5. Oct 2, 2016 #4


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    I've answer this in a previous thread, so read that first and then you can ask more questions here.
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