三角函数的积分计算技巧

Integral Calculation Skills of Trigonometric Functions

三角有理函数的积分求解是微积分中一个很重要的内容。在三角函数的积分中,将被积函数化为已知的三角函数和用变量代换是计算三角函数积分的两种重要的算法。但是对于三角函数的积分算法不止仅限于以上的两种,我们应该根据被积函数的特征,掌握更多的求解三角函数积分的方法。本文用实际的例子给出五种处理三角有理函数积分的方法与技巧,分别是利用三角函数恒等变形、变量代换法、万能换元、奇偶性、递推法。

The integral solution of trigonometric rational function is a very important content in calculus. In the integration of trigonometric functions, converting the integrand into known trigonometric functions and using variable substitution are two important algorithms for calculating the inte-gration of trigonometric functions. But for the trigonometric function integration algorithm is not limited to the above two;we should master more methods to solve the trigonometric function in-tegration according to the characteristics of the integrand. In this paper, five methods and tech-niques for processing trigonometric rational function integration are given by practical examples. They are the same deformation of trigonometric function, variable substitution method, universal substitution method, parity and recursion method.