  In this paper, we prove that the 1D Cauchy problem of the compressible
Navier-Stokes equations admits a unique global classical solution $(\rho,\rm
u)$ if the viscosity $\mu(\rho)=1+\rho^{\beta}$ with $\beta\geq0$. The initial
data can be arbitrarily large and may contain vacuum.
  Some new weighted estimates of the density and velocity are obtained when
deriving higher order estimates of the solution.
