In this study, we present a new closed form for the generalized integral $\int_0^1 \frac{\mathrm{Li}_2(z) \ln(1+az)}{z} \, \mathrm{d}z,$ where $a \in \mathbb{C} \setminus (-\infty, -1)$ and $\mathrm{Li}_2(z)$ is the dilogarithm function. This generalization is achieved by leveraging our established findings in conjunction with Vălean’s results. Furthermore, we provide explicit closed forms for associated integrals, prove a transformation formula for double infinite series, expressing them as the sum of the square of an infinite series and another infinite series. We utilize this relationship to derive a novel closed form for the generalized series $\sum_{k=1}^\infty \frac{ \zeta\left(m, \frac{rk-s}{r}\right) }{(rk-s)^m},$ for $\Re(m) > 1$, $r, s \in \mathbb{C}$, where $r \neq 0$, $rk \neq s$, for any positive integer $k$, and $\zeta(s, z)$ denotes the Hurwitz zeta function. Utilizing Hermite's integral representation for $\zeta(s, z)$, we derive a family of integrals from this series.