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Interesting but tricky integration problem

  1. Apr 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Evaluate the integral, (x^2+3x-8/x^2+16)dx, without using partial fraction expansion. Now this has really confused me. I know that partial fraction expansion is not viable because the mumerator has a higher power overall than the denominator

    3. The attempt at a solution

    S x^2 /(x^2 + 16) dx + S 3x /(x^2 + 16) dx - S 8 /(x^2 + 16) dx

    i have split it up like this, but i am not sure if this counts as a partial fracion expansion?

    Next id use the rule, that the integral of (dx/a^2+x^2)=1/a tan(-1) x/a +c. But there are several x^2 on top, so how this does fit in.
    It probably easier than it looks, any help would be much appreciaed. Thanks
  2. jcsd
  3. Apr 16, 2009 #2


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    Science Advisor
    Homework Helper

    Use polynomial division to divide x^2+3x-8 by x^2+16 first.
  4. Apr 16, 2009 #3


    Staff: Mentor

    Minor point -- the numerator does NOT have a higher power than the denominator. The degree of each is 2.
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