求不定积分 ∫ dx ⼀ √(e^2x-1)过程,答案是arccose^-x+C

2024-11-27 04:13:56
推荐回答(2个)
回答1:

回答2:

∫ dx / √(e^2x-1)
let
e^x = secy
e^x dx = tany(secy) dy
dx = tany dy

∫神耐 dx /游尘春兄枝 √(e^2x-1)
= ∫ dy
= y + C
= arcsec(e^x) + C
=arccos(e^(-x)) + C