Integration(difficult)

👨🏻‍🏫 學術台數學

CRebecca

2011-08-17 9:34 am

1. Evaluate ∫_(0,∞) (sinx - x + x³)/[x³(x²+1)] dx
2. Evaluate ∫_(0,∞) sinx /(1+e^x) dx
(Exact forms not infinite series)

圖片參考：http://imgcld.yimg.com/8/n/HA06881079/o/701108170011013873444320.jpg

更新1:

Corr. 1. Evaluate ∫_(0,∞) (sinx - x - x³)/[x³(x²+1)] dx

回答 (3)

用戶9112

2011-08-20 5:15 am

✔ 最佳答案

http://i1090.photobucket.com/albums/i376/Nelson_Yu/3-2.jpg
http://i1090.photobucket.com/albums/i376/Nelson_Yu/4-1.jpg

圖片參考：http://i1090.photobucket.com/albums/i376/Nelson_Yu/3-2.jpg

圖片參考：http://i1090.photobucket.com/albums/i376/Nelson_Yu/4-1.jpg

👍 1 👎 0

mathmanliu

2011-08-20 8:36 am

Q1. 積分 [e^(ix) - ix - ix^3 -1 + 0.5x^2 ]/(x^5+x^3)就可避免 zero pole的問題
Q2. 積分 e^(ix) /(1+e^x), 繞右半長方形(strip,高2π i ), 求虛部就好

👍 0 👎 0

doraemonpaul

2011-08-17 2:25 pm

2. http://eqworld.ipmnet.ru/en/auxiliary/inttrans/FourSin3.pdf

👍 0 👎 0

收錄日期: 2021-04-23 23:24:31
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110817000051KK00110

檢視 Wayback Machine 備份