8. Evaluate the indefinite integral. (Use C for the constant of integration.) \[ \int \frac{e^{u}}{\left(3-e^{u}\right)^{2}} d u \]

To evaluate the indefinite integral \[ \int \frac{e^{u}}{\left(3-e^{u}\right)^{2}} d u, \] we can use the substitution method. Let \( v = 3 - e^u \). Then, the differential \( dv = -e^u du \), or equivalently, \( du = -\frac{dv}{e^u} = -\frac{dv}{3 - v} \). Now rewrite the integral in terms of \( v \): \[ \int \frac{e^{u}}{(3 - e^{u})^2} du = \int \frac{-1}{v^2} dv, \] where we substituted \( e^u \) with \( 3 - v \). The integral of \(-\frac{1}{v^2}\) is: \[ \frac{1}{v} + C, \] Substituting back for \( v \): \[ \frac{1}{3 - e^{u}} + C. \] Thus, the final result is: \[ \int \frac{e^{u}}{\left(3-e^{u}\right)^{2}} d u = -\frac{1}{3 - e^{u}} + C. \]