∫xlnx dx = ?
要steps plz
integration
2012-03-08 2:56 am
回答 (3)
2012-03-08 3:09 am
✔ 最佳答案
∫xlnxdxLet u=lnx, du=dx/x.Let dv=xdx, v=x²/2.By ∫udv=uv-∫vdu, ∫xlndx=(lnx)(x²/2)-∫(x²/2)(dx/x)=x²lnx/2-(1/2)∫xdx=x²lnx/2-(x²/2)/2=x²lnx/2-x²/4=(2x²lnx-x²)/4=x²(2lnx-1)/4
參考: I Hope This Can Help You ! ^_^ ( From Me )
2012-03-12 3:06 am
∫xlnxdx Let u=lnx, du=dx/x. Let dv=xdx, v=x²/2. By ∫udv=uv-∫vdu, ∫xlndx =(lnx)(x²/2)-∫(x²/2)(dx/x) =x²lnx/2-(1/2)∫xdx =x²lnx/2-(x²/2)/2 =x²lnx/2-x²/4 =(2x²lnx-x²)/4 =x²(2lnx-1)/4
2012-03-08 4:29 am
圖片參考：https://www4c.wolframalpha.com/Calculate/MSP/MSP34421a0d2g6e91b582e600003ad03949f1ci38ga?MSPStoreType=image/gif&s=55&w=423&h=294
PS 這裡的log(x)是ln(x)
2012-03-11 22:50:11 補充：
https://mail.google.com/mail/h/q62un1qv57zi/?view=att&th=136023c6f688201d&attid=0.1&disp=inline&realattid=file0&safe=1&zw
2012-03-11 22:55:51 補充：
https://docs.google.com/open?id=0BxSM_TQVsWJkY3hndFpSdnRSYlczWndHMXp4T1dSZw
2012-03-11 22:56:50 補充：
2012-03-11 22:56:26 補充的Link才是有效的。
參考: Wolfram Alpha
收錄日期: 2021-04-13 18:33:45
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120307000051KK00541