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Homework Help: Odd integral

  1. Feb 2, 2009 #1
    1. The problem statement, all variables and given/known data

    I want to deal with this int((5+10y^4)dy/(y+2y^5))

    2. Relevant equations

    integration, substitution, partial fractions?

    3. The attempt at a solution

    I tried a bunch of random things. I think it hs to do with substitution because if I make u=y+2y^5, du/dy=1+10y^4 which is strikingly similar to the numerator, so there must be a cancellation. this integral is part of a dif equation, but i cant see to go past this! i know for sure this is the correct set up because i used my calculator to integrate and it solved the differential equation.
  2. jcsd
  3. Feb 2, 2009 #2


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    Uh, the ratio of those two polynomials is a VERY SIMPLE THING. Can you find it? Factor them.
  4. Feb 2, 2009 #3
    Try this :
    5 + 10y^4 = 4 + 1 + 10y^4

    after you get it, think of a crafty substitution
  5. Feb 2, 2009 #4


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    Think of a crafty cancellation before you do the crafty substitution.
  6. Feb 3, 2009 #5
    jesus i feel like a complete retard. i hate when i dont get something as obvious.i factored both and cancelled that nasty factor and then everything went smooth, thanks a bunch gentlemen.
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