Question

Integral e^x/(1+e^2x) dx

Answer 1

e^x = t
e^xdx = dt
Your integral become:
dt/1+t^2

Answer 2

@ncorrea92

Answer 3

arctg t +C = arctg e^x +C

Answer 4

Im sorry i don't understand it

Answer 5

make change of variable
e^x = t
e^xdx = dt

Answer 6

Your integral become:
dt/1+t^2

Answer 7

and just solve it

Answer 8

(e^x)^2=e^2x

Answer 9

another (probably more complicated) approach is to use the trig sub\[e^x=\tan x\]