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

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Answer 1 · 2015-05-26T07:19:58

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

$arctan(e^x)+C$

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