How do you find the integral of #(1/(e^x+e^-x))dx#?

1 Answer
May 26, 2015

it's not by part, just a little trick and then substitution

#int1/(e^x+e^(-x))dx#

Start by multiplying numerator and denominator by #e^x#

#int e^x/(e^(2x)+1)dx#

Substitute #t = e^x#

#dt = e^xdx#

#int1/(t^2+1)#

We can see the derivative of #arctan(t)#

#[arctan(t)]+C#

Substitute back

#arctan(e^x)+C#