求不定积分2x+4/x^2+2x+6 dx
答案:1 悬赏:10 手机版
解决时间 2021-03-19 09:27
- 提问者网友：谁的错
- 2021-03-18 16:55
求不定积分2x+4/x^2+2x+6 dx
最佳答案
- 五星知识达人网友：野慌
- 2021-03-18 17:13
∫(2x+4)/(x^2+2x+6) dx
= ∫(2x+2)/(x^2+2x+6) dx + 2∫dx/(x^2+2x+6)
=ln|x^2+2x+6| + 2∫dx/(x^2+2x+6)
consider
x^2+2x+6 = (x+1)^2 +5
let
x+1 = √5.tany
dx =√5(secy)^2 dy
∫dx/(x^2+2x+6)
=(√5/5)∫ dy
=(√5/5)y
=(√5/5)arctan[(x+1)/√5]
∫(2x+4)/(x^2+2x+6) dx
=ln|x^2+2x+6| + 2∫dx/(x^2+2x+6)
=ln|x^2+2x+6| + (2√5/5)arctan[(x+1)/√5] + C
= ∫(2x+2)/(x^2+2x+6) dx + 2∫dx/(x^2+2x+6)
=ln|x^2+2x+6| + 2∫dx/(x^2+2x+6)
consider
x^2+2x+6 = (x+1)^2 +5
let
x+1 = √5.tany
dx =√5(secy)^2 dy
∫dx/(x^2+2x+6)
=(√5/5)∫ dy
=(√5/5)y
=(√5/5)arctan[(x+1)/√5]
∫(2x+4)/(x^2+2x+6) dx
=ln|x^2+2x+6| + 2∫dx/(x^2+2x+6)
=ln|x^2+2x+6| + (2√5/5)arctan[(x+1)/√5] + C
我要举报
如以上问答信息为低俗、色情、不良、暴力、侵权、涉及违法等信息，可以点下面链接进行举报！
大家都在看
推荐资讯