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Integration by substitution?

  1. Jan 11, 2008 #1
    1. The problem statement, all variables and given/known data
    I want to integrate (1+x)/(1-x)

    2. Relevant equations

    3. The attempt at a solution
    I have looked at many examples of substitution method - this one appears simple but Im not finishing the last step.....

    - I know you must first take u=(1-x)
    - Then du = -dx

    what happens with the numerator (1+x) as this would be the integral of -(1+x)du/u

    id be very grateful if you could run me through the steps for this please.

  2. jcsd
  3. Jan 11, 2008 #2


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    Staff Emeritus
    Science Advisor

    You need to simplify the fraction first: dividing 1+ x by 1- x gives -1+ 2/(1-x)= -1- 2/(x-1). It's easy to integrate "-1" and to integrate -2/(x-1), let u= x-1.
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