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Homework Help: Integral (need help getting started

  1. Feb 15, 2009 #1
    1. The problem statement, all variables and given/known data
    [tex]\int(x^4+2x^2+x+1)/(x^2+1)^x[/tex]


    3. The attempt at a solution
    am I supposed to multiply out the denominator then do u sub?
     
  2. jcsd
  3. Feb 15, 2009 #2
    nevermind i think its arctan
     
  4. Feb 16, 2009 #3

    HallsofIvy

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    Science Advisor

    It isn't anything if the exponent on that denominator is really "x"! If it was supposed to be "2", I recommend dividing the fraction our so that you have a polynomial plus a "proper fraction" of the form [tex]\frac{ax+ b}{x^2+ 1}[/tex]. That you divide into two parts: [tex]\frac{ax}{x^2+1}[/tex] and [tex]\frac{1}{x^2+ 1}[/tex]. The first uses the simple substitution [tex]u= x^2+ 1[/tex] and the second is an arctan.
     
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