不定积分习题:∫1/[√(9-x^2)]dx

题目

不定积分习题:∫1/[√(9-x^2)]dx

答案

令x=3cost
∫1/[√(9-x^2)]dx
=∫1/[√(9-9costcost)]d(3cost)
=∫sint^(-1)(-3sint)/3dt
=-∫dt
=-t+C
=-arccos(x/3)+C