Question

求积分∫1/根号下(2-3x^2)dx

Answer 1

∫1/√(2-3x^2) dx

let

x =√(2/3) .siny

dx = √(2/3) cosy dy

∫1/√(2-3x^2) dx

=∫√(2/3) cosy dy/(√2 cosy)

=(1/√3)∫dy

= (1/√3) y + C

=(1/√3) arcsin(√3x/√2) + C