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Homework Help: Very difficult integral

  1. Jan 8, 2009 #1
    1. The problem statement, all variables and given/known data

    \int \frac{x}{\sqrt{x^4 + 10 x^2 - 96 x - 71}}\ \mbox{d}x

    3. The attempt at a solution
    I don't see what's useful completing a square, gonio substitution (or even a useful substitution). Does anyone have an idea?
  2. jcsd
  3. Jan 8, 2009 #2
    The denominator can be replaced as [{(x^2+5)^2/96 - 1}^2 + 5]^2.

    P.S. That /96 is to the whole (x^2+5)^2 expression.
  4. Jan 8, 2009 #3
    That's a degree 16 polynomial, there MadHawk.

    Was this a homework problem, Dirk? Could you provide some context as to where it arose. According to the integrator at http://integrals.wolfram.com/index.jsp?expr=x/Sqrt[x^4+10*x^2-96*x-71]&random=false, it would seem the integral as you have written it cannot be expressed in elementary terms.
  5. Jan 8, 2009 #4


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    Your expression isn't even of the same degree as the denominator in the original expression:eek:

    I think you'd better double check your math on that one!:wink:
  6. Jan 8, 2009 #5


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    Hmmm... are you sure that [itex]-96x[/itex] is supposed to be there?
  7. Jan 8, 2009 #6
    Well, it was just pure innocent fun. The actual quantity under root is (x^2+5)^2 - 96(x+1). From here, I think, it can be done. Sorry folks, for the joke above.
  8. Jan 9, 2009 #7
    Yes, this IS the correct integral. Furthermore there is an exact solution which can be written in elementary functions. What can you advice me to do? Is Madhawks suggestion the way to tackle this integral?

    Where are Dick and HallsofIvy? Or did I scare them away :wink:
    Last edited: Jan 9, 2009
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