Question

How do I find this? ∫((e^x)/(2+e^x))dx

Answer 1

use u-substitution where u = 2+e^x
and since the derivative of e^x is e^x,
du = e^x
so in terms of 'u' the integral is
∫(1/u)du (since the contents of u are on the bottom and the contents of du are on top)

and the integral of 1/u = ln(u) + C, so put x back into the equation using u's value

ln(u) + C = ln(2+e^x) + C
(C doesn't change because it just represents an unknown constant)