Can anyone integrate these? They have stumped me! Any help would be appreciated

1 / (1 + e^x)

and

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

Can anyone integrate these? They have stumped me! Any help would be appreciated

1 / (1 + e^x)

and

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

For the second integral, use u substitution:

/

|e^x

|-------------dx

|1+e^(2x)

/

/

e^x dx |
---|

1+(e^x)^2 |

/

Now, let u = e^x

so du = e^x dx

Substituting, we have:

/

|1

|------------du

|1 + u^2

/

= arctan(u) + C

= arctan(e^x) + C