積分求解 ∫ 2/u(u^2+1)?
回答 (2)
2018-01-23 7:59 am
✔ 最佳答案
Sol設2/[u(u^2+1)]=a/u+(bu+c)/(u^2+1)
2=a(u^2+1)+(bu+c)u
u=0 =>
2=a
2=2(u^2+1)+bu^2+cu
b=－2
c=0
2/[u(u^2+1)]=2/u－2bu/(u^2+1)
∫ 2/u(u^2+1)du
=∫ 2/udu－∫ 2u(u^2+1)du
=∫ 2/udu－∫ u^2/(u^2+1)du
=∫ 2/udu－∫(u^2+1)/(u^2+1)du
=2ln｜u｜－ln(u^2+1)+c
2018-01-22 7:41 pm
令x=u^2+1 dx=2udu
收錄日期: 2021-04-30 22:36:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20180122110339AAUH3zP