Question

What is the integral of `(e^(2x))/(1+e^(2x))`?

Answer 1

`1/2 ln (1+e^(2x))+C`

`int e^(2x)/(1+e^(2x) dx`

Integrate by substitution. Let `u=1+e^(2x)`. Thsi makes `du = 2e^(2x)`

`int e^(2x)/(1+e^(2x)) dx = 1/2 int 1/u du = 1/2 ln abs u +C`

`= 1/2 ln (1+e^(2x)) +C`