Integration of an inverse polynomial

  • Thread starter Ado
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  • #1
Ado
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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 !
 

Answers and Replies

  • #2
marcusl
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You have not written a valid integral. You must reformulate your problem.
 
  • #3
Ray Vickson
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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 !

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 .
 
  • #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.
 
  • #5
Ado
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Never mind! ;)
Thanks for your replies!
 

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