Galerkin discretizations of integral equations in R d require the evaluation of integrals I = R S (1) R S (2) g(x, y)dydx where S (1) , S (2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for x = y and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occuring in integral equations. We construct a family of quadrature rules Q N using N function evaluations of g which achieves

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... al convergence |I − Q N | ≤ C exp(−rN γ ) with constants r, γ > 0.