Square formulas, implicit and enclosed algorithms of the integration on the non-obvious scale

For numerical integration of $y_i=f(x_i)$, $x\in[a,d]$, $i=\overline{0,n}$, functions that are arranged on nonregular scale with particulars new classes are presented of explicit square formulas and implicit algorithms based on calculation of integrals $I_i^{i+1}=\int\limits_{x_i}^{x_{1+i}}f(x)dx$ $i=\overline{0,n}$, from algebraic systems of linear algebraic equadons.