1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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 :) .
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook