It is shown that the nonlinear Schrödinger equation describing pulse propagation in optical fibers in the presence of a properly space-tailored damping or amplification is exactly integrable. A simple transformation of variables is given which transforms the inhomogeneous nonlinear Schrödinger equation into the standard form with constant coefficients, thus generating new explicit bright and dark soliton solutions in the cases of anomalous and normal dispersion, respectively.