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U Substitution Problem

  1. Feb 25, 2014 #1
    1. The problem statement, all variables and given/known data

    ∫2x√(2x-3) dx

    2. Relevant equations



    3. The attempt at a solution
    u=2x
    du=2 dx

    1/2∫u√(u-3) du

    Am I on the right track with this? I'm not really sure what to do next.
     
  2. jcsd
  3. Feb 25, 2014 #2
    Sort of. u= the inside of the square root
    u=2x-3
    du=2dx
    dx=du/2 or 1/2

    ∫1/2 2xu^1/2 dx
    the 2's cancel out.
    now it should look like
    ∫x*u^1/2 and integrate that. and plug in the value for u after your done integrating
    Becareful, because if i remember correctly. after integrating ∫x*u^1/2
    Since we have an x. you have to solve for it, and plug it in.
    u=2x-3 <-Solve the x

    2x-3=0 2x=3
    x=3/2
     
    Last edited: Feb 25, 2014
  4. Feb 25, 2014 #3
    Thanks so much!
     
  5. Feb 25, 2014 #4

    SteamKing

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    If u = 2x -3, then 2x = u + 3, so that your integral after substitution has only u in it.

    Your integrand becomes (u+3)*SQRT(u)*du/2

    You don't want an integrand which mixes x and u after substitution.
     
  6. Feb 25, 2014 #5
    thanks for the correction
     
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