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Homework Help: Easy integration by parts help

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data

    integral of ln(2x +1)

    2. Relevant equations
    I know this is an easy problem but i can not seem to figure out what to substitute for my U and my dV. I was thinking on making my U= 2x+ 1. but then my problem is what would my dV be? ln U? lnx? the ln is throwing me off a bit. im not sure what it is the ln of.

    3. The attempt at a solution

    U= 2x+1 dV= lnU (?)
    dU/2= dx V= 1/U (?)
  2. jcsd
  3. Sep 18, 2010 #2


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    When you want to integrate by parts, a good choice for u is that part which has a simple derivative, and for v that part which is easy to integrate. So you can choose ln(2x+1)=u and 1=dv/dx

  4. Sep 18, 2010 #3
    ok perfect. got the answer. I have seen it done the way you just showed & i have also seen it done a different way. If we first substitute
    p= 2x+1
    dp/2 = dx
    then once this is done we have 2 integral ln(p).
    now from here we do integration by parts by choosing
    u= ln(p) dV= dp
    du= 1/p V= p

    now is there any difference between the two? or any situations where one will work and the other wont?
  5. Sep 19, 2010 #4


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    Both methods have the same result, but substituting first 2x+1 by p is much simpler. Do not forget to plug in 2x+1 for p at the end.

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