Question

Integral de 1/ e^x +e^-x

Answer 1

∫1/(eˣ + e⁻ˣ) dx
Sea u= eˣ
du/dx= eˣ
dx= du/eˣ = du/u

∫1/(eˣ + e⁻ˣ) dx = ∫1/(u + u⁻¹) du/u
= ∫1/(u²+1) du

Sabiendo que la derivada de arctan x= 1/x²+1
 ∫1/(u²+1) du = arctan(u) + c
= arctan(eˣ) + c