淺析有理函數(shù)和三角有理式的不定積分問(wèn)題

淺析有理函數(shù)和3角有理式的不定積分問(wèn)題

摘  要

本文考慮有理函數(shù)和3角有理式的不定積分問(wèn)題，在數(shù)學(xué)分析教材中講解的基本方法的基礎(chǔ)上，又歸納出了幾種方法。熟練掌握和應(yīng)用這些方法對(duì)于解決有理函數(shù)和3角有理式的不定積分問(wèn)題非常重要，有利于進(jìn)1步拓寬思路，大大提高不定積分的運(yùn)算能力。

關(guān)鍵詞：不定積分，有理函數(shù)，3角有理式.

Abstract
 
This paper considers the issue on indefinite integral of rational functions and rational expressions of trigonometric functions. Based on the basic methods in the textbooks on mathematical analysis, some useful methods and techniques for computation are summarized, which are very important to promote the ability to calculate indefinite integrals.

Key words: Indefinite Integral, rational functions, rational expressions of trigonometric functions
  
目   錄                                                                                                               
前言…………………………………………………………………………………1
1 有理函數(shù)的不定積分
1.1待定系數(shù)法………………………………………………………………………2
1.2微分法……………………………………………………………………………8
1.3換元法……………………………………………………………………………9
2 3角有理式的不定積分
2.1換元法……………………………………………………………………………11
2.2組合積分法………………………………………………………………………16
  2.3  湊微分法 …………………………………………………………………17
3致謝…………………………………………………………………………………18
4參考文獻(xiàn)……………………………………………………………………………19

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