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Integration by completing the square

  1. Mar 20, 2012 #1
    1/x^2 + 4x + 5



    1) Completing the square
    x^2 + 4x/2 + 5 - 4
    (x+2)^2 +1

    After this I know what to do??
     
  2. jcsd
  3. Mar 20, 2012 #2

    Mark44

    Staff: Mentor

    What's your question? You're asking about an integration problem - what is the problem?

    x2 + 4x + 5 = x2 + 4x + 4 + 1 = (x + 2)2 + 1
     
  4. Mar 20, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What you wrote is
    [tex]\frac{1}{x^2}+ 4x+ 5[/tex]
    but I feel sure you meant
    [tex]\frac{1}{x^2+ 4x+ 5}= \frac{1}{(x+2)^2+ 1}[/tex]

    Now, do you know an integral formula for
    [tex]\int \frac{dx}{x^2+a^2}[/tex]?
     
  5. Mar 20, 2012 #4

    Mark44

    Staff: Mentor

    I misread that 1/ part as "problem #1". Didn't occur to me that he meant the reciprocal of something.
     
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