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Anti derivative homework

  1. Mar 18, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the antiderivative of x^2 / [ (x-1)(x^2 + 4x +5)].

    2. Relevant equations

    3. The attempt at a solution

    I first tried multiplying the denominator to get x^2 / x^3 + 3x^2 + x - 5 ... I noticed that the numerator is almost the derivative of the denominator, and if I can alter the expression to get du/u I can integrate it by using some form of ln |u|. I've tried several ways but I don't know where to go from here or what to do.
  2. jcsd
  3. Mar 18, 2007 #2


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    Almost? I wouldn't say that. Not even close.

    I thought about it, and it certainly doesn't look like an easy one to solve. I then put it in Maple to see what the solution looks like, and it's definitely looks tricky to get too.

    What methods have you studied so far?

    I think you can probably pull off partial fractions as your first steps actually. Oh, it looks doable now. I always think substitutions first. I'm still practicing my integrals. :frown:
  4. Mar 19, 2007 #3

    Gib Z

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    You have some nasty stuff on your hands. Did it say to show working? If it just said "Find the antiderivative...", www.calc101.com can help :)

    partial Fractions, i might be wrong, gave me this:

    [tex]\frac{x^2}{(x-1)(x^2 +4x+5)} = \frac{9x+5}{10(x^2+4x+5)} + \frac{1}{10(x-1)}[/tex].

    The 2nd bit is easy, the first bit isn't fun >.<.

    Your going to have to do some completing the square, then let u = x+2 and hopefully our nice friend arctan will help you with the rest.
  5. Mar 19, 2007 #4


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    Sounds like a solid plan to me.
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