Using Fetter's analytical approximation, [f_{1}left(ho^{prime} ight)=frac{ho^{prime}}{sqrt{left(1+ho^{prime 2} ight)}}] for the solution of equation (11.5.23) with (s=1), calculate

Using Fetter's analytical approximation,

\[f_{1}\left(ho^{\prime}\right)=\frac{ho^{\prime}}{\sqrt{\left(1+ho^{\prime 2}\right)}}\]

for the solution of equation (11.5.23) with \(s=1\), calculate the energy (per unit length) associated with a quantized vortex line of unit circulation. Compare your result with the one quoted in (11.5.26).