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Integral Question

  1. Feb 27, 2008 #1
    1. The problem statement, all variables and given/known data

    Hi, I'm trying to take the integral of x/(x^2-2x+5) dx but I'm not sure what to do.

    2. Relevant equations



    3. The attempt at a solution

    I started by completeing the square in the denominator giving me the integral of x/((x-1)^2+4)) dx but I am not sure where to go from there. I have the correct answer for it but I need to understand the steps involved getting there.

    EDIT: Okay, after spending a decent amount of time on this problem I finally look for some place to get help, and 5 minutes later I think I come up with a solution.

    First, I set u = x^2 - 2x +5, du/2 - 2/2 = x. Substituted back in which gave me (1/2)integral( (du-2)/u ) which I then split into (1/2)integral(du/u) - (1/2)integral(2/u).

    Taking the integral of the first part gave me (1/2)ln(x^2 - 2x +5). For the second half, I substitued the u values back into the equation which gave me: -(1/2)integral(2/(x^2 - 2x + 5). I completed the square in the denominator which gave me -integral( 1/((x-1)^2+4 ).

    Integrating that part of the equation gives me -(1/2)arctan((x-1)/2).

    So my final answer is (1/2)ln(x^2 - 2x +5) - (1/2)arctan((x-1)/2) + C. Can someone please confirm my steps? Sorry if my work is hard to follow. I wasn't sure how to make the proper symbols and my time is short :)
     
    Last edited: Feb 27, 2008
  2. jcsd
  3. Feb 27, 2008 #2

    Dick

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    Homework Helper

    That's right.
     
  4. Feb 27, 2008 #3
    Hell, that seemed clever(or I suck)

    I would've done partial fraction decomposition, and heaven knows NO ONE likes doing that
     
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