題目如上 希望能有詳細算式 thx
更新1:
∫(x^2/1+x^2)dx sorry題目沒打清楚
請問一題不定積分的問題
回答 (4)
2011-12-10 6:51 am
2011-12-10 1:51 am
∫x^2/(1+x^2)dx
Sol
∫dx/(1+x^2)
Set x=Tanw
dx=Sec^2 wdw
∫dx/(1+x^2)
=∫Sec^2 wdw/Sec^2 w
=∫dw
=w+c
=ArcTanx－c
So
∫x^2/(1+x^2)dx
=∫(1+x^2－1)/(1+x^2)dx
=∫dx-∫dx/(1+x^2)
=x－ArcTanx+c
Sol
∫dx/(1+x^2)
Set x=Tanw
dx=Sec^2 wdw
∫dx/(1+x^2)
=∫Sec^2 wdw/Sec^2 w
=∫dw
=w+c
=ArcTanx－c
So
∫x^2/(1+x^2)dx
=∫(1+x^2－1)/(1+x^2)dx
=∫dx-∫dx/(1+x^2)
=x－ArcTanx+c
2011-12-10 1:04 am
會否是:
∫x^2 dx/(1+x^2) ?
∫x^2 dx/(1+x^2) ?
收錄日期: 2021-04-30 16:21:25
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111209000010KK03891