高等数学一元函数不定积分求法研究

A Study of the Methods of Calculating Indefinite Integration of One-Variable Functions in Advanced Mathematics

高等数学一元函数积分求法是多元函数积分求法的基础,在高等数学的学习中起举足轻重的作用.根据调查研究发现,许多学生对高等数学一元函数的多种不定积分方法混淆不清,机械套用公式,套用积分方法的现象屡见不鲜,没有真正理解高等数学一元函数积分方法的真谛.系统研究一元函数的不定积分的方法、本质特点,积分准则,结合代表性例题,给出求不定积分的基本步骤,对激发学生学好高等数学的兴趣,为后续课程的学习奠定扎实的基础,提高教学质量,都具有十分重要的意义[1].

Calculating integration of one-variable functions in advanced mathematics is the preliminary of calculating integration of multivariable functions, and plays a vital role in the study of advanced mathematics. According to research, many students are confused by the variety of methods to Indefinite integrate one-variable functions in advanced mathematics. Quite a few of them would inflexibly and blindly apply the formulate and the algorithms without understanding the essence of the methods of integrating one-variable functions in advanced mathematics. It is of great significance for stimulating students＇ interest in studying advanced mathematics well, building solid foundation for study in the future,and improving teaching quality, to systematically study the methods and nature of Indefinite integration of one-variable functions as well as its guide-lines, and provide the basic steps and general procedures of Indefinite integration with reference to typical examples.