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Integral of (1-e^-x)^(1/2)?

  1. Sep 9, 2010 #1
    1. The problem statement, all variables and given/known data
    what is the integral of (1-e^-x)^(1/2)?
    HELP~~


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 9, 2010 #2

    ehild

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    What do you think about the substitution t^2=1-e^(-x)= ?

    ehild
     
  4. Sep 9, 2010 #3

    CompuChip

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    I think it is
    [tex]
    \frac{\sqrt{1-e^{-x}} \left(e^{x/2} x-2 \sqrt{e^x-1}+2 e^{x/2} \log
    \left(-e^{-x/2} \sqrt{e^x-1}-1\right)\right)}{\sqrt{e^x-1}}
    [/tex]

    Is that what you got as well?

    By the way, I find this a rather hard calculus problem for an introductory physics class.
     
  5. Sep 9, 2010 #4

    ehild

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    I was too lazy to check either formula. I left e-x unchanged, used the substitution 1-e-x =t2,

    [tex]dx=\frac{2tdt}{1-t^2}[/tex]

    I also got the logarithm of a fraction plus a constant times the square root. The problem can be solved, and you are right, it should rather be at "Calculus and Beyond"

    ehild
     
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