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Integral of sqrt(1 + x^4+ 2x^2)

  1. Aug 18, 2010 #1
    1. The problem statement, all variables and given/known data
    sqrt(1 + x^4+ 2x^2)

    2. Relevant equations

    3. The attempt at a solution
    k so i need a lead on this one, maybe some kind of substition, i am not quite adept with finding the integrals of a square root function with polynomials in it
  2. jcsd
  3. Aug 18, 2010 #2


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    Here's a bit of a hint. When you expand (x+1)^2, what do you get?
  4. Aug 18, 2010 #3


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    This problem is rigged to simplify VERY nicely :smile:

    Let x2=u and you should see it more easily.
  5. Aug 18, 2010 #4
    x^2 + 2x + 1
  6. Aug 18, 2010 #5
    ohhh hmm
  7. Aug 18, 2010 #6
    ok i see it now, but if x^2 = u then dx x= du and then dx = du/x does that makes sense ?
  8. Aug 18, 2010 #7
    You can't put du/x inside the integral, the point of the substitution is to get rid of the x's....look at x^4+2x^2+1...there is a way to simplify it similar to how you would simplify x^2+2x+1...you won't need a substitution and then the answer is easy.
  9. Aug 18, 2010 #8
    sorry i am dumb i got it
  10. Aug 18, 2010 #9


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    Oh yes sorry I never meant for you to make a substitution in the classic sense of solving an integral, but to make the substitution since u2+2u+1 is easily distinguishable as (u+1)2
  11. Aug 18, 2010 #10


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    (1 + x4 + 2x2)1/2

    = [(1 + x2)2]1/2

    = (1 + x2 )

    Now find the integration of (1 + x2)dx
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