An integration

👨🏻‍🏫 學術台數學

CRebecca

2011-08-15 7:50 pm

Evaluate ∫_(0,∞) ln(x)/(1+x^n) dx, for integer n > 1

回答 (3)

doraemonpaul

2011-08-23 7:10 am

✔ 最佳答案

http://en.wikipedia.org/wiki/Beta_function#Properties
http://en.wikipedia.org/wiki/Beta_function#Derivatives

2011-08-22 23:10:09 補充：

圖片參考：http://i212.photobucket.com/albums/cc82/doraemonpaul/yahoo_knowledge/improperintegration/goodimproperint9.jpg

參考資料：
method similar to http://hk.knowledge.yahoo.com/question/question?qid=7011081100197 + formula from http://en.wikipedia.org/wiki/Beta_function#Properties + http://en.wikipedia.org/wiki/Gamma_function#General

👍 1 👎 0

用戶9112

2011-08-20 3:06 pm

實在是太大意了,只好告退.

👍 0 👎 0

mathmanliu

2011-08-20 8:28 am

答案是 (-1)cos(p) [p/sin(p)]^2, 其中 p=π/n, n > 1 ( n 為"實數")

👍 0 👎 0

收錄日期: 2021-04-24 10:33:46
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110815000051KK00355

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