用换元法求1⼀(x√(9-x눀))的定积分

2024-11-25 14:25:27
推荐回答(1个)
回答1:

∫dx/(x√(9-x^2))

let
x=3siny
dx =3cosydy
∫dx/(x√(9-x^2))
=∫dy/(3siny)
= (1/3)ln|cscy - coty | +C
= (1/3)ln| 3/x - √(9-x^2)/x | +C