dfinite integration
回答 (1)
2011-04-08 3:28 am
✔ 最佳答案
∫x^2/(9+x^2)dxSol
∫x^2/(9+x^2)dx
=∫1－9/(9+x^2)dx
=∫dx－∫9/(9+x^2)dx
Set x=3Tanw
Tanw=x/3
w=arcTan(x/3)
9+x^2=9+9Tan^2 w=9Sec^2 w
dx=3Sec^2 wdw
∫9/(9+x^2)dx=∫9/(9Sec^2 w)*3Sec^2 wdw
=3∫dw
=3w+c1
=3arcTan(x/3)+c1∫x^2/(9+x^2)dx
=∫dx－∫9/(9+x^2)dx
=x－3arcTan(x/3)－c1
=x－3arcTan(x/3)+c
收錄日期: 2021-04-20 00:26:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110407000051KK00801