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Integrating [e^x / (1 + e^2x ) ]dx

  1. Feb 15, 2006 #1
    integ [e^x / (1 + e^2x ) ]dx.can someone show me how to solve this by using 1 / (1 + x^2 ) formula??
    pls.........
     
  2. jcsd
  3. Feb 15, 2006 #2

    arildno

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    What have you done?
     
  4. Feb 15, 2006 #3
    i think of arranging it to be [e^x / (1 + {e^x}^2 ) ] but cannot related it to 1 / 1 + x^2
     
  5. Feb 15, 2006 #4

    arildno

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    Good move! :smile:
    Now, is it a clever change of variables that leaps into your eyes?
     
  6. Feb 15, 2006 #5
    for the differentiation arctan x result is 1 / 1 + x^2 but for this ques how about the e^x on the numerator??
     
  7. Feb 15, 2006 #6
    HINT: You can "get rid" of the [tex]e^x[/tex] in the numerator by a simple change of variables.
     
  8. Feb 15, 2006 #7
    is it just subs e^x by u then diff du = e^x dx ??
     
  9. Feb 15, 2006 #8
    Yes, that is correct. :smile:
     
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