Propositions to widen the frequency bandwidth of an integrator

The transfer function, T, of an ideal integrator is 1/taus. Its phase, equal to -pi/2, is independent of the frequency value, whereas the gain decreases in a proportional way with this value of omega. However, on the one hand, it is usually necessary to limit the DC gain so that the transfer function takes the shape T = k/(1 + ktaus). On the other hand, the active components such as operational amplifiers (op. amps.) or current feedback operational amplifiers are not perfect and they bring a supplementary pole at a high frequency. Therefore the bandwidth where the integrator phase is equal to -pi/2 is included between omega_MIN and omega_MAX. For a couple DC gain and an op. amp. given, increasing the ratio omega_MAX/omega_MIN to a maximum is proposed.