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Integral Help Please

  1. Feb 2, 2006 #1
    I am having a heck of a hard time with this integral... I have tried everything what I can think of:

    [itex]\int \! \left( {e^{x}}+{e^{-x}} \right) ^{-1}{dx}[/itex]

    I tried integration by parts... I ended up getting [itex]\left( {e^{x}} \right) ^{-1}[/itex] even thought the right answer, according to Maple and my graphing calculator is [itex]\arctan \left( {e^{x}} \right)[/itex]

    I then tried using substitution... I made [itex]u={e^{x}}[/itex] and then [itex]{\it du}={e^{x}}{\it dx}[/itex] but that doesn't help me, because I don't have [itex]{e^{x}}{\it dx}[/itex] but rather I have [itex]{\frac {{\it dx}}{{e^{x}}}}.[/itex]

    Can anyone point me in the right direction? Thanks!
     
  2. jcsd
  3. Feb 2, 2006 #2
    make this substituion u=e^x
    then (e^x)dx=du ---> udx=du ---> dx=du/u
    the int becomes (1/(u+1/u))*(du/u) ---> (1/(1+u^2))*du the int is then arctan = arctan[e^x]
    sorry but i don't knwo this latex language to write it in a more elegant way.
     
  4. Feb 2, 2006 #3
    Thank you so much! It worked :) .
     
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