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Integration problem

  1. Mar 22, 2015 #1
    1. The problem statement, all variables and given/known data
    integrate 1/(1+e^x) dx
    2. Relevant equations


    3. The attempt at a solution
    firstly i let t=1+e^x
    and then i come to : integrate 1/(t^2-1)
    and then i put t=secx
    .
    .
    .
    but then the final ans is -1/2 ln | 2/e^x +1 |

    it should be 1 instead of 2, i hv checked for the steps for so many times, but found nothing wrong
     
  2. jcsd
  3. Mar 22, 2015 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You have done the substitution wrong.

    If [itex]t= 1+ e^x[/itex] then [itex]dt= e^xdx= (t- 1)dx[/itex] so that [itex]\frac{1}{t- 1}= dx[/itex].

    [tex]\int \frac{1}{1+ e^x}dx= \int \frac{1}{t} \frac{dt}{t- 1}= \int \frac{1}{t(t- 1)} dt[/tex]

    NOT [itex]\int \frac{1}{t^2- 1} dt[/itex]
     
  4. Mar 22, 2015 #3

    Zondrina

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    Homework Helper

    Perhaps you should multiply the top and bottom of the expression by ##e^{-x}## and see what happens when you substitute ##u = e^{-x}##.
     
  5. Mar 22, 2015 #4
    then you can use partial fraction i.e. create (t)- (t-1) in the numerator
     
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