1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integration by substitution

  1. Nov 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Integrate [tex]\int[/tex][tex]\frac{dz}{1+e^z}[/tex] by substitution

    2. Relevant equations



    3. The attempt at a solution

    I chose u=(1+[tex]e^{z}[/tex]) so du/dz=[tex]e^{z}[/tex] and dz=du/[tex]e^{z}[/tex].

    Therefore, [tex]\int[/tex][tex]\frac{1}{u}[/tex] [tex]\frac{du}{e^{z}}[/tex]

    I plug z=ln(u-1) in for z, so [tex]\int[/tex][tex]\frac{1}{u}[/tex] [tex]\frac{du}{u-1}[/tex]

    From here though I don't know how to integrate. Can anyone help me with the next step?
     
  2. jcsd
  3. Nov 10, 2009 #2

    Mark44

    Staff: Mentor

    Rewrite 1/(u(u -1)) as a sum: A/u + B/(u - 1). Solve for A and B so that the two expressions are identically equal. This is called partial fractions decomposition.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...