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: Hyperbolic Functions

  1. Mar 18, 2009 #1
    1. I am asked to calculate [tex]\int \frac{dx}{cosh(x)}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    I know that [tex]\frac{1}{cosh(x)}[/tex] is equivalent to "sech(x)" which by definition is [tex]\frac{2}{e^x+e^{-x}}[/tex].

    I'm confused & I don't know which one I need to use for this question:

    [tex]\int sech(x) = 2tan{-1}(tanh(\frac{x}{2}))[/tex]

    [tex]\int \frac{2}{e^x + e^{-x}} = 2tan^{-1}(e^x)[/tex]

    Any help would be greatly appreciated.
    Last edited: Mar 18, 2009
  2. jcsd
  3. Mar 18, 2009 #2
    The two answers you got only differ by a constant of [tex]\frac{\pi}{2}[/tex]. Recall that the indefinite integral is only defined up to a constant, so both solutions are correct.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook