Question

How do you evaluate the definite integral `int (e^x)/(1+e^x)` from `[0,1]`?

Answer 1

`=ln( (1+e)/2)`

Explanation:

note that `d/dx(ln (1+e^x)) = (e^x)/(1+e^x)`

So

`int_0^1 (e^x)/(1+e^x) \ dx`

`=int_0^1 d/dx(ln (1+e^x)) \ dx`

`=[ ln (1+e^x)]_0^1`

`=ln( (1+e)/2)`