求不定積分和定積分的方法研究
Study on indefinite integral and definite integral method


目錄
引言 4
第一章 求不定積分的幾種方法 7
1.1利用分部積分法求不定積分 8
1.2利用對(duì)偶法求不定積分 10
1.3不定積分計(jì)算中“1”的巧妙利用 8
1.4待定系數(shù)法求不定積分 12
第二章 求定積分的幾種方法 13
2.1利用換元法求定積分 13
2.2 利用被積函數(shù)奇偶性 13
結(jié)論 16
致謝 17
參考文獻(xiàn) 18


摘要 不定積分和定積分是數(shù)學(xué)分析的一個(gè)重要內(nèi)容，我們常用的求不定積分的方法有：直接積分法，換元積分法和分部積分法等. 不定積分在理論上十分簡(jiǎn)明，但利用基本積分公式及性質(zhì)，只能求出一些通常情況的積分，對(duì)于比較復(fù)雜的積分，在運(yùn)算上則有一定難度。這時(shí)我們需要尋求其他方法，以便更好的幫助解決這類問題，本文通過一些例題介紹求不定積分的四種方法，分部積分法，對(duì)偶法又叫解方程組法，在積分過程中對(duì)“1”的巧妙利用，和待定系數(shù)法。還有求定積分的兩種常用方法，換元法和函數(shù)奇偶性。

關(guān)鍵詞：不定積分 分部積分 對(duì)偶法 “1”的靈活使用 待定系數(shù)法 定積分 換元法 奇偶性



Study on indefinite integral and definite integral method
Abstract Indefinite integral and definite integral is an important part of mathematical analysis, we always used the method of solving indefinite integral are: direct integration method，integration by substitution， Integrate by parts，and so on .the indefinite integral in theory very simple, but the use of the basic integral formulas and properties, can only solving a few simple questions, there are some difficulties in solving the more complex questions. Then we need to find other ways to better help solve this problem, this paper describes four methods of indefinite integrals, integration by parts, dual method called solution of equations method, the integration process of the "1 "the clever use, and the method of undetermined coefficients. There are two common methods to solve definite integral，methods of substitution and parity of function.
Key words：Indefinite integral Division of integral Dual method Flexibly use “1” method of Undetermined coefficient definite integral Method of substitution Parity

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