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Homework Help: Cant do this integral sub

  1. Sep 28, 2010 #1
    integral of (x+25)(x/4+6)^7 dx


    no foiling out the power

    i thought mayeb putting it as (x+25)((x/4+6)^2)^3.5 dx
    and then sub : u = x^2/16 + 3x +36 and du = x/8 + 3 dx and 8du = x +24 dx

    but its x+25 that we got ... so yea
     
  2. jcsd
  3. Sep 28, 2010 #2

    Dick

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    What's wrong with u=x/4+6? Can't you express x+25 in terms of u?
     
  4. Sep 28, 2010 #3

    fzero

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    There's a much more obvious substitution that turns the integrand into a sum of monomials. Make the denominator (almost) as simple as possible.
     
  5. Sep 28, 2010 #4
    well then du = dx ... umm how could that be correct?
     
  6. Sep 28, 2010 #5
    If u = x/4 +6 then du is not equal to dx.
     
  7. Sep 28, 2010 #6
    well if u = x/4 +6 then the closest to x+25 is 4u = x+24
     
  8. Sep 28, 2010 #7
    sorry 4du = dx
     
  9. Sep 28, 2010 #8
    The point is to get rid of all the x. You don't need it to have the form c*u where c is some constant.
     
  10. Sep 28, 2010 #9

    Dick

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    i) du isn't equal to dx and ii) how do you know it couldn't work if you haven't tried it?
     
  11. Sep 28, 2010 #10
    would i be able to do that with integration by parts?
     
  12. Sep 28, 2010 #11
    i did it gives me u = x/4 + 6 and du = dx/4

    dont know where to go form there
     
  13. Sep 28, 2010 #12

    fzero

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    u = x/4 + 6 is the same as x = 4u - 24. Rewrite the entire integral in terms of u and du.
     
  14. Sep 28, 2010 #13
    ok well i get
    4* integral (4u-1)((4u-2)/4)^7 du
    1/4^6 * integral (4u-1)(4u-2)^7 du

    and now im stuck ... once again -_-
     
  15. Sep 28, 2010 #14
    You have:

    x/4 + 6 = u (the substitution we did to make the denominator nice)
    x + 25 = 4u + 1
    dx = 4 du

    Use this.
     
  16. Sep 28, 2010 #15

    fzero

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    You have an algebra mistake in your substitution. u = x/4 + 6 and x = 4u - 24 mean that

    (x+25)(x/4+6)^7 dx = ( 4u -24 + 25) (u)^7 ( 4 du)
     
  17. Sep 28, 2010 #16
    ya so i have 4* integral (4u+1)(u^7) du
     
  18. Sep 28, 2010 #17
    so its equal to :

    4[ (4(x/4+6)^9)/9 + ((x/4+6)^8)/8] + c ?
     
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