高数,求不定积分,凑微分法求此题

2024-11-17 09:33:06
推荐回答(1个)
回答1:

let
u = √(1-x^2)
du = -[x/[√(1-x^2)] dx
∫ x/[(2-x^2)√(1-x^2) ] dx

=-∫ du/(1 + u^2)
=-arctanu + C
=-arctan[√(1-x^2)] + C