  Earlier work introduced a method for obtaining indefinite $q$-integrals of
$q$-special functions from the second-order linear $q$-difference equations
that define them. In this paper, we reformulate the method in terms of
$q$-Riccati equations, which are nonlinear and first order. We derive
$q$-integrals using fragments of these Riccati equations, and here only two
specific fragment types are examined in detail. The results presented here are
for $q$-Airy function, Ramanujan function, Jackson $q$-Bessel functions,
discrete $q$-Hermite polynomials, $q$-Laguerre polynomials, Stieltjes-Wigert
polynomial, little $q$-Legendre, and big $q$-Legendre polynomials.
