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Integration-problem using u-substitution

  1. Oct 8, 2013 #1
    1. The problem statement, all variables and given/known data

    ∫(ex)/(2ex+2)dx

    2. Relevant equations

    and im told to use:

    u=2ex+2

    3. The attempt at a solution

    If i use u=2ex+2 as the task says;

    du/dx = 2ex and dx =du/2ex

    ∫(ex)/(u)du/2ex=∫(1)/(2u)du=1/2ln|u| + c =1/2ln|2ex+2|

    according to the book the answer should be 1/2ln|ex+1|

    however if i use u =ex+1 and write the integral 1/2∫(ex)/(ex+1)dx i get the correct answer. Where am i going wrong?
     
    Last edited: Oct 8, 2013
  2. jcsd
  3. Oct 8, 2013 #2

    BruceW

    User Avatar
    Homework Helper

    they are both correct, the only difference is the constant of integration, which you don't know anyway. Hint: write 2ex+2 as a constant times ex+1, and then make use of the properties of logarithms to see that you get the same answer (without caring about the constant of integration, since you don't know it anyway).
     
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