Optimal approximation of operators with power-logarithmic kernels

This paper presents the construction of an optimal quadrature formula in the Sobolev space L(m)2 (0; x) for integrals with power-logarithmic kernels. Formulas for calculating the coefficients of the optimal quadrature formula are derived. An example is considered to validate the optimal quadrature formula. The results of the example are compared with the exact solution. The results were used to determine the compliance of this optimal quadrature formula with the theoretical foundations.