A special assessment within a city of the metropolitan class shall not be declared void or invalid because the city council sitting as a board of equalization has included in the total cost of the improvement (1) the cost of inspection under the direction of the city engineer, (2) the cost of such grading, filling, or street repairs incidental to such improvement, (3) the additional cost of maintenance or repair of such improvement included in the contract for such work, and (4) the cost of removing obstructions and removing and lowering pipes owned and controlled by the city.