Definite Integration

Let for \(x \in \mathbb{R}, S_{0}(x)=x, S_{k}(x)=C_{k} x+k \int_{0}^{x} S_{k-1}(t) d t\), where


\(C_{0}=1, C_{k}=1-\int_{0}^{1} S_{k-1}(x) d x, k=1,2,3, \ldots\) Then \(S_{2}(3)+6 C_{3}\) is equal to ____________.