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

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)