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Integral equation based analysis of scattering (both acoustic and electromagnetic) is well known and has been studied for several decades. Analysis typically proceeds along the following lines: representation of the geometry using a collection of triangles, representation of physics using piecewise constant basis function defined on each triangle, and then solving the resulting discrete system. In the past few decades, this area has seen several improvements in algorithms that reduce the computational complexity of analysis. But, as we delve into higher order isogeometric analysis (IGA), these algorithms are bogged down by the cost of integration. In this paper, we seek to address this challenge. Our candidate for modeling geometry and physics are subdivision basis sets. The order of these basis sets is sufficiently high to make the challenge apparent. We will present a methodology to ameliorate the cost for both acoustic and electromagnetic integral equations and demonstrate its efficacy.