electric fields - Kirchoff's rules and inductance

Can Kirchoff's loop rule be applied in a scenario involving an inductor? Kirchoff's loop rule states that the closed loop integral of E dot dl is equal to zero. But, in a situation with an inductor, a changing magnetic flux is involved which means that the electric field is nonconservative and the closed loop integral of E dot dl is not zero. I watched MIT professor Walter Lewin's lectures on inductance and Faraday's law and he emphatically states that Kirchoff's loop rule cannot be used in this situation. Yet, most textbooks (University Physics, Giancoli, Berkeley Physics, etc.) use the loop rule anyways (setting the "voltage drop" across the inductor to be -L*di/dt and setting the sum of all the voltage drops to be zero). Now I am very confused. Any help would be greatly appreciated!