`int e^u/(1 - e^u)^2 du ` Evaluate the indefinite integral.

You need to use the following substitution  `1 - e^u= t` , such that:

`1 - e^u= t=>-e^u du = dt => e^u du = -dt`

`int (e^u*du)/((1-e^u)^2) = -int (dt)/(t^2)`

`-int (dt)/(t^2) = 1/t + c`

Replacing back `1 - e^u ` for t yields:

`int (e^u*du)/((1-e^u)^2) = 1/(1 - e^u) + c`

Hence, evaluating the indefinite integral, yields `int (e^u*du)/((1-e^u)^2) = 1/(1 - e^u) + c.`