  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 extension is achieved by leveraging our established findings in
conjunction with V\u{a}lean'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 generalized integral series from this series.
