Symbolic-numeric integration of univariate expressions based on sparse regression

The majority of computer algebra systems (CAS) support symbolic integration using a combination heuristic algebraic and rule-based (integration table) methods. In this paper, we present hybrid (symbolic-numeric) method to calculate the indefinite integrals univariate expressions. Our is broadly similar Risch-Norman algorithm. primary motivation for work add functionality modern CAS (the manipulation packages SciML, Scientific Machine Learning ecosystem Julia programming language), which designed numerical machine learning applications. part our based on candidate terms generation (ansatz methodology borrowed from Homotopy operators theory) combined with expression transformations provided by underlying CAS. numeric uses sparse regression, component Sparse Identification Nonlinear Dynamics (SINDy) technique, find coefficients terms. We show that system can solve large variety common problems only few dozen basic rules.