  We show that integrals involving log-tangent function, with respect to
certain square-integrable functions on $(0, \pi/2)$, can be evaluated by some
series involving the harmonic number. Then we use this result to establish many
closed forms relating to the Riemann zeta function at odd positive integers. In
addition, we show that the log-tangent integral with respect to the Hurwitz
zeta function defines a meromorphic function and that its values depend on the
Dirichlet series $\zeta_h(s) :=\sum_{n = 1}^\infty h_n n^{-s}$, where $h_n =
\sum_{k=1}^n(2k-1)^{-1}$.
