  In this paper we construct a dissipative quintessential cosmic inflation. For
this purpose, we add a multiplicative dissipative term in the standard
quintessence field Lagrangian. We consider the specific form of dissipation as
the time integral including the Hubble parameter and an arbitrary function that
describes the dissipative properties of the quintessential scalar field.
Inflation parameters and observables are calculated under slow-roll
approximations and a detailed calculation of the cosmological perturbations is
performed in this setup. We consider different forms of potentials and
calculate the scalar spectral index and tensor-to-scalar ratio for a constant
as well as variable dissipation function. To check the reliability of this
model, a numerical analysis on the model parameters space is done in
confrontation with recent observational data. By comparing the results with
observational joint datasets at 68% and 95% confidence levels, we obtain some
constraints on the model parameters space, specially the dissipation factor
with e-folds numbers N = 55 and N = 60. As some specific results, we show that
the power-law potential with a constant dissipation factor and N = 60 is mildly
consistent with observational data in some restricted domains of the model
parameter space with very small and negative dissipation factor and a
negligible tensor-toscalar ratio. But this case with N = 55 is consistent with
observation considerably. For power-law potential and variable dissipation
factor as $Q = {\alpha}\phi^n$, the consistency with observation is also
considerable with a reliable tensor-to-scalar ratio. The quadratic and quartic
potentials with variable dissipation function as $Q = {\alpha}\phi^n$ are
consistent with Planck2018 TT, TE, EE+lowE+lensing data at the 68% and 95%
levels of confidence for some intervals of the parameter n.
