递推法在医药高等数学不定积分计算方面的应用  

Mathematical Induction In the Application of Indefinite Integral Calculation for Medical Higher Mathematics

作　　者：吕佳萍[1] 孙向荣[2] 

机构地区：[1]南京中医药大学数学教研室,南京210023 [2]南京邮电大学理学院

出　　处：《数理医药学杂志》2015年第11期1731-1733,共3页Journal of Mathematical Medicine

基　　金：国家自然科学基金10926104;南京中医药大学青年自然科学基金13XZR35资助项目

摘　　要：不定积分是医药高等数学中积分学里的重要内容,根据被积函数和积分变量的形式,我们可以将被积表达式进行适当改写,运用积分方法和积分公式来确定结果。被积函数和积分变量的形式千变万化,不定积分的计算难度、方法和技巧也不一样。如果被积函数中出现了自然数n,随着n的变化,积分结果有一定的变化规律,我们就可以用递推法来计算不定积分。三角函数和对数函数是基本初等函数,当被积函数是高次的三角函数或对数函数时,本文用递推法得出了一些不定积分公式。The indefinite integral is the important part of the integral for medical higher mathematics,ac-cording to the integrand and integral variables,we can rewrite the integrand appropriately and use integral method and integral formula to determine the results.The integrand and the integral variables have diferrent forms,so computational difficulty,methods and techniques of integration is not the same.If the integrand has occurred in the natural number n,with the variation of n,the integration results show some regularity,we can use mathematical induction to calculate the indefinite integral.Trigonometric functions and logarithmic func-tions are basic elementary functions,when the integrand is high degree trigonometric function or high degree logarithm function,we get some indefinite integral formulas with mathematical induction.

关 键 词：递推法 三角函数 对数函数 不定积分 

分 类 号：O172.2[理学—数学]