  Two recently introduced quadrature schemes for weakly singular integrals
[Calabr\`o et al. J. Comput. Appl. Math. 2018] are investigated in the context
of boundary integral equations arising in the isogeometric formulation of
Galerkin Boundary Element Method (BEM). In the first scheme, the regular part
of the integrand is approximated by a suitable quasi--interpolation spline. In
the second scheme the regular part is approximated by a product of two spline
functions. The two schemes are tested and compared against other standard and
novel methods available in literature to evaluate different types of integrals
arising in the Galerkin formulation. Numerical tests reveal that under
reasonable assumptions the second scheme convergences with the optimal order in
the Galerkin method, when performing $h$-refinement, even with a small amount
of quadrature nodes. The quadrature schemes are validated also in numerical
examples to solve 2D Laplace problems with Dirichlet boundary conditions.
