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: Indefinite integral

  1. May 9, 2005 #1
    How do I find the indefinite integral of 1/[(e^x)+(e^-x)] ???

    Do I have to multiply by [(e^x)-(e^-x)]/[(e^x)-(e^-x)] to eliminate the denominator???? !
     
  2. jcsd
  3. May 9, 2005 #2
    are you trying to do:
    [tex]\int\frac{dx}{e^x+e^{-x}}[/tex]

    if so, for a=b=c:
    [tex]\int\frac{dx}{e^{ax}+e^{-bx}}=\int\frac{dx}{e^{cx}+e^{-cx}}=\frac{tan^{-1}(e^{cx})}{c}+C[/tex]
    i hope that helps
     
  4. May 9, 2005 #3

    I dont get it :confused:
     
  5. May 9, 2005 #4
    [tex] \frac{1}{e^x + e^{-x}} = \frac{1}{\frac{(e^x)^2+1}{e^x}}[/tex]

    Can you go from there?
     
  6. May 9, 2005 #5

    James R

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    This might help you:

    [tex]\frac{e^x + e^{-x}}{2} = \cosh x[/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook