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Homework Help: Integration (by substitution?)

  1. May 25, 2005 #1
    how can i integrate:
    x^2+7x+10 dx
    x+2

    i assume it's by substitution, but i can't work it out.

    sorry for the formatting, btw
     
  2. jcsd
  3. May 25, 2005 #2
    Factor the top, it cancels.
     
  4. May 25, 2005 #3
    (x+5)(X+2) =x+5
    (x+2)
    I don't know nothing about integrate. But I think you have to factor the trinomial then divide.
     
  5. May 25, 2005 #4
    Note the singularity at x = -2, it cant be integrated in a region containing this point.
     
  6. May 25, 2005 #5

    dextercioby

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    Not really.It can't be defined at x=-2,which means that automatically that point is excluded from the integration domain.

    Daniel.
     
  7. May 25, 2005 #6
    thanks. should've seen it.
     
  8. May 25, 2005 #7
    Does the integral

    [tex] \int_{-3}^1 \frac{x^2+7x+10}{x+2} \ dx [/tex] exist, dex? As its written?
     
  9. May 25, 2005 #8

    dextercioby

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    I don't know.U'll have to break it into 2 and evaluate each limit.(I wasn't talking about a definite integral,so your (counter)example is useless).

    Daniel.
     
  10. May 25, 2005 #9
    Its the same thing.
     
  11. May 25, 2005 #10

    HallsofIvy

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    However, the integral is a "smoothing" operation. The integral of a function with removable discontinuity exists and is exactly the same as the integral of the function with the discontinuity removed.
     
  12. May 25, 2005 #11
    whozum do you agree that x^2 is integratable, what about [tex]\frac{(x^2)(x+1)}{x+1}[/tex]?
     
  13. May 25, 2005 #12
    Theyre both integrable, just the latter isnt continuous.
     
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