  Numerical integration is a classical problem emerging in many fields of
science. Multivariate integration cannot be approached with classical methods
due to the exponential growth of the number of quadrature nodes. We propose a
method to overcome this problem. Tensor-train decomposition of a tensor
approximating the integrand is constructed and used to evaluate a multivariate
quadrature formula. We show how to deal with singularities in the integration
domain and conduct theoretical analysis of the integration accuracy. The
reference open-source implementation is provided.
