This paper studies the integration problem in differential fields that may involve quantities reminiscent of the Weierstrass $\wp$ function, which are defined by a first-order nonlinear differential equation. We extend the classical notion of special polynomials to elements of Weierstrass-like extensions and present algorithms for reduction in such extensions. As an application of these results, we derive some new formulae for integrals of powers of $\wp$.

翻译：本文研究微分域中的积分问题，这些微分域可能涉及与Weierstrass $\wp$ 函数相关的量，这些量由一阶非线性微分方程定义。我们将经典的特殊多项式概念推广到Weierstrass型扩张的元素，并提出了在此类扩张中的约化算法。作为这些结果的应用，我们推导出$\wp$函数幂次积分的一些新公式。