Implicit square formulas

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