n次三角函数不定积分的探究

Investigation of Indefinite Integrals of Trigonometric Functions of the n Degree

摘要: 结合具体的实例，通过低次方三角函数不定积分的研究，总结，逐步深入到研究n次三角。最终探究，${\displaystyle \int {\sin }^{m}x}\text{d}x,{\displaystyle \int {\cos }^{n}x}\text{d}x$ 以及${\displaystyle \int {\sin }^{m}x\cdot {\cos }^{n}x}\text{d}x$ 的显式结果及其证明。

Abstract: Combined with concrete examples, through the study of the indefinite integral of low power trigonometric function, summary, and step by step in-depth study of n trigonometry. The explicit results of ${\displaystyle \int {\sin }^{m}x}\text{d}x$ , ${\displaystyle \int {\cos }^{n}x}\text{d}x$ and ${\displaystyle \int {\sin }^{m}x\cdot {\cos }^{n}x}\text{d}x$ and their proofs are discussed.