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Integration of an inverse polynomial

  1. Jun 9, 2017 #1

    Ado

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    • Member advised that the homework template must be used
    Hello,

    I want to integrate this expression :

    ∫ (x5 + ax4 + bx3 + cx2 + dx)-1

    between xmin>0 and xmax>0

    a is positive but b, c and d can be positive or negative.

    I have no idea to integrate this expression... Do you have methods to do this ?

    Thanks in advance !
     
  2. jcsd
  3. Jun 9, 2017 #2

    marcusl

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    You have not written a valid integral. You must reformulate your problem.
     
  4. Jun 9, 2017 #3

    Ray Vickson

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    You can solve the problem when you are given numerical values of ##a,b,c,d##, by finding the roots of the polynomial using numerical methods, and so write the integrand in partial fractions. However, for general symbolic values of ##a,b,c,d## you are out of luck, because it is a rigorously-proven theorem that there is NO finite formula for the roots of a general polynomial of degree 5 or more. See, eg., https://en.wikipedia.org/wiki/Abel–Ruffini_theorem .
     
  5. Jun 9, 2017 #4

    marcusl

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    Sorry, I took dx to be the differential variable but I see now that you are using "d" as a constant, and that there must be an implied differential dx in your equation. Please ignore my post.
     
  6. Jun 9, 2017 #5

    Ado

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    Never mind! ;)
    Thanks for your replies!
     
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