A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite rules for conversion to and from associated nested sums are discussed. We also include a short discussion comparing the holonomic systems approach and the differential field approach. For simplification to rational integrands, we give a comprehensive list of univariate rationalizing transformations, including transformations tuned to map the interval $[0,1]$ bijectively to itself.

翻译：本文简要概述了用于嵌套积分计算的一些计算机代数方法，重点讨论被积函数包含平方根的嵌套积分。文中探讨了与相关嵌套和相互转换的重写规则，并简要比较了完整系统方法与微分域方法。针对简化至有理被积函数，我们给出了单变量有理化变换的全面列表，其中包括了为将区间 $[0,1]$ 双射映射至自身而优化的变换。