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Integration by partial fractions- a quadratic

  1. May 12, 2009 #1

    TG3

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    The problem statement, all variables and given/known data

    Integrate: (x-1) / (X^2 - 4x +5)

    The attempt at a solution

    Normally I would try to factor this into something like (x-1) (x+3) (That's an example completely unrelated to this problem.)
    However, as no easy factors quickly occurred to me I did a run through of the quadratic equation, and got 4 +or- (16- 4x1x5)^.5 / 2 = 4 + (-4)^.5 / 2

    At my basic level of Calculus, imaginary numbers are taboo, so I want to avoid the square root of a negative number.

    Am I missing an obvious factoring, am I performing the quadratic wrong (that would be embarrassing) or should I try another technique? And if another technique.... what is it?
     
  2. jcsd
  3. May 12, 2009 #2

    rock.freak667

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    well if x^2 - 4x +5=0 has no real roots, then you need to express the partial fraction in the form (ax+b)/(Ax^2+Bx+C)
     
  4. May 12, 2009 #3

    Dick

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    The technique you are missing is to complete the square in the denominator, x^2-4x+5=(x-2)^2+1. Substitute u=x-2. Can you see how to go from there?
     
  5. May 12, 2009 #4

    Dick

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    Quoi? That's the same form as the original integrand!?? It's no partial fraction at all.
     
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