Additive Decompositions for Symbolic Integration and Summation

    Additive decompositions are useful to determine integrability and ($q$)-summability and to construct telescopers.
    In this talk, we review some recent developments for additive decompositions with rationality, integrability, ($q$)-summability and minimality. Furthermore, we present an additive decomposition in primitive towers of straight and flat types. The decomposition enables us to compute some integrals of logarithmic functions without solving Risch's equation.
    This is joint work with Shaoshi Chen and Hao Du.