When it is difficult or impossible to integrate a function analytically, or when an analytical expression for the function is not available, numerical methods are used to obtain approximations for the observed integrals. Weakly singular integrals occur when the function is unbounded and the value of the integral is finite. There are various methods for calculating such integrals, which can be grouped into three categories. This work introduces the Gauss-Legendre formula (for regular integral), the Telles method and its generalisation, and the sigmoid transform and its generalisation. These methods fall under the category of coordinate transformation for evaluating univariate weakly singular integrals. Namely a transformation to the integrand is applied to smooth out the singularity and thus evaluate integrals with higher accuracy.
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