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Math Help - Integral Question

  1. #1
    Junior Member
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    Integral Question

    I asked this in an earlier question, but it was overlooked.

    2) xdx/x^4 + x^2 + 1

    I set u = x^2
    du = 2x
    = 1/2 Integral of du/u^2+u+1

    And I STILL can't solve it!

    I want to isolate U^2+1 to make that arctan(u), but I don't see a way.

    Cheers!
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  2. #2
    MHF Contributor
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    Hi

    Use the "canonical" form
    u+u+1 = (u+1/2)+3/4

    Set t=u+1/2 then v=2t/sqrt(3)
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    \frac{x}{x^{4}+x^{2}+1}=\frac{4x}{\left( 2x^{2}+1 \right)^{2}+3}, so put 2x^2+1=\sqrt3t and you'll get the arctan form.
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