Hi,
I'm after integrating the function 1 / (e^x + e^-x); how exactly would I go about this? Some kind of substitution seems like the best route, but I'm not entirely sure what.
Thanks,
Stewart
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Hi,
I'm after integrating the function 1 / (e^x + e^-x); how exactly would I go about this? Some kind of substitution seems like the best route, but I'm not entirely sure what.
Thanks,
Stewart
Welcome to the forums.
I believe this is 1/2 hyperbolic secant, or sech(x)/2. Aren't hyperbolic trig functions analagous to standard trig functions? In other words, I think you'd use the same method that would be used to integrate sec(x)/2. Just my recollection from a long time ago......:)
Also, isn't this the same as
(e^x + e^-x)^(-1)
I think you can simplify this a lot more:
1/ e^x + e^-x
=
1/ (e^x + 1/e^x)
= 1/ (e^x^2 + 1 / e^x)
= e^x/ e^x^2 + 1
u = e^x
du = e^x (cancels with e^x on top)
= 1/ (u^2+1)
= arctan(e^x)
Looks like (1/a)arctan(x/a) to me, but I could have easily messed up somewhere (this is tough without paper and pencil).
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