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Homework Help: Integrating the natural log

  1. Feb 1, 2009 #1
    1. The problem statement, all variables and given/known data
    How would I begin to integrate ln(t+1) from 0 to e^2x?

    2. Relevant equations
    d/dx[log base a of u]=1/(lna)u du/dx

    Can the original equation be manipulated to use this derivative?

    3. The attempt at a solution
    Not sure where to start.
  2. jcsd
  3. Feb 1, 2009 #2


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    It's the sort of problem where you could actually guess the antiderivative, but if you can't, integrate by parts.
  4. Feb 7, 2009 #3
    It's an integration by part question. First, use a substitution to get it to one variable instead of a polynomial in the logarithm.
    Substitute (I'm going to revert the limits in the end to the original variable, so you know):
    Integrate of ln(w)dw
    u=ln(w) and dv=dw
    du=(1/w)*dw and v=w

    now evaluate at your endpoints:
    You can probably simplify this some more, but there it is.
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