`int2 sqrt[1-e^[-x]]e^[-x] dx`

Let

`u = 1 − e^(-x)`

The derivative of u is

`(du)/dx = 0 − (-e^(-x)) = e^(-x)`

So the differential du is:

`du = e^(-x)dx`

We substitute to give:

`int2 sqrt[1-e^-x] e^-x dx=2 int sqrtu\ du`

`=2int u^[1/2]\ du`

`=2((2)/(3))u^[3/2]+K`

`=4/3(1-e^-x)^[3/2]+K`

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