We extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension. Both of the reductions are incorporated into one algorithm. As an application, we present an additive decomposition in rationally hyperexponential towers. The decomposition yields an alternative algorithm for computing elementary integrals over such towers. The alternative can find some elementary integrals that are unevaluated by the integrators in the latest versions of Maple and Mathematica.

翻译：本文将有理函数域上超指数函数的壳约化和核约化推广至单项式扩张。将两种约化合并为单一算法。作为应用，我们给出有理超指数塔中的加法分解。该分解为计算此类塔上的初等积分提供了替代算法。该替代算法能求出最新版Maple和Mathematica积分器无法计算的某些初等积分。