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Integration (e)

  1. Mar 7, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex]\int dx/(e^{x}\sqrt{1-e^{-2x}}) [/tex]

    2. Relevant equations



    3. The attempt at a solution
    I have absolutely no idea of how to start the problem, any help is greatly appreciated!
    thanks!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 7, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    Try a substitution of maybe u=e-x. Then you should get it into a form where the anti-derivative should be easily found.
     
  4. Mar 8, 2010 #3

    Mark44

    Staff: Mentor

    Also, note that 1/ex = e-x.
     
  5. Mar 8, 2010 #4
    hmm, can i get a little more hint? if i do a u sub. of u = e[tex]^{-x}[/tex], how do i get rid of
    e[tex]^{-2x}[/tex]? I have tried do a u sub. of u = [tex]\sqrt{1-e^{-2x}}[/tex], but i ended up getting the [tex]\int du/e^{-x}[/tex], which i dont know how to proceed after this. What am i doing wrong?
     
  6. Mar 8, 2010 #5

    rock.freak667

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    Homework Helper

    e-2x=(e-x)2, so in terms of u it is?
     
  7. Mar 8, 2010 #6

    Mark44

    Staff: Mentor

    Doesn't e-x*e-x = e-2x?
     
  8. Mar 8, 2010 #7
    o boy, that was embarrassing lol
    just want to make sure, is the answer cos[tex]^{-1}[/tex](e[tex]^{-x}[/tex]) + C?
     
  9. Mar 8, 2010 #8

    rock.freak667

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    Homework Helper

    That should be correct.

    I think -sin-1(e-x)+C should work as well.
     
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