Closed-form solution for the change in impedance of a single-turn coil located inside a conducting cylindrical tube is presented in the paper. The axis of the coil coincides with the axis of the tube. The electric conductivity and magnetic permeability of the tube are power functions of the radial coordinate. The system of equations for the vector potential is solved by the method of Fourier cosine transform. Equations for the transformed components of the vector potential in free space are solved in terms of the modified Bessel functions of order one. The ordinary differential equation for the transformed component of the vector potential in the tube is solved by means of the confluent hypergeometric function. Results of numerical calculations are presented in the paper.