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Calculate the integral

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

    [tex]\int [/tex](sin (e^(-2x))) / e^(2x)


    3. The attempt at a solution

    so i set
    u=e^2x
    du=(e^2x)(2) dx

    im kinda stuck on how to get rid of the e^-2x
     
  2. jcsd
  3. Feb 1, 2009 #2

    arildno

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    Dearly Missed

    Set u=e^-2x instead.
    Therefore, du/dx=-2u, that is dx=-du/2u

    Use this to simplify your integrand!
     
  4. Feb 1, 2009 #3
    k using u=e^-2x
    du=-2 (e^-2x) dx

    so...

    -1/2 [tex]\int[/tex] sin u du

    -1/2 (-cos u) + c is that right???
     
  5. Feb 1, 2009 #4

    Dick

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    Sure. But there is a simpler way to write (-1/2)*(-cos(u)).
     
  6. Feb 1, 2009 #5
    so final answer is cos u /2
     
  7. Feb 1, 2009 #6

    Dick

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    cos(u)/2+C. Use more parentheses. cos u /2 can also be read cos(u/2).
     
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