In Chap. 12 , three types of unsolvable integrals were identified for the most basic photo- and photothermal reactions. The insolvability of those integrals made the solutions of their respective rate-laws not possibly achievable by analytical means. We will attempt here to bring approximated solutions to these integrals by using the Maclaurin expansion series [1]. The approximation using first-order expansion to the primary photoreaction (with \( {\varepsilon}_Y^{\lambda_{n- isos}}=0 \) ) has previously been reported in Sect. 11.6 . Such a first-order expansion treatment is the only level of approximation reported in the literature [2]. The approximation in the present chapter will be performed with second-order expansion series. It will be applied to the series of unsolvable integrands laid out in the previous chapter. The second-order expansion is employed here because treatments based on third and higher expansion orders are not practically useful since they will ultimately lead to complicated integrands that do not have known antiderivatives.