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Leibniz notation

  1. Sep 25, 2013 #1
    1. The problem statement, all variables and given/known data
    Using Leibniz's rule to find dy/dx for
    y = integral of e^-t from interval: [ln(x) to ln(x+1)]


    2. Relevant equations



    3. The attempt at a solution
    dy/dx = e^-(ln(x+1))*(1/(1+x))-e^-(ln(x))*(1/x)
    = (x+1)/(1+x) - (x/x)
    = 0

    Im not sure what I'm doing wrong or how to properly use leibniz's rule... i checked wolfram alpha and my answer doesn't look right.

    also side question, my teacher manages to simplify integral of (x^2)/(x^2+a^2)^2 to (integral 1/(x^2+a^2) - a^2*integral(1/(x^2+a^2)^2)
    if you have a clue on how he reaches to that conclusion i would appreciate it.
     
  2. jcsd
  3. Sep 25, 2013 #2

    arildno

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    e^-(ln(x))=1/x, not x as you've written. Similarly for ln(x+1)
     
  4. Sep 25, 2013 #3

    arildno

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    As to your second quastion:

    Replace your numerator with the device x^2=(x^2+a^2)-a^2
     
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