令x=sinΘdx=cosΘdΘx=1/2,Θ=π/6x=-1/2,Θ=-π/6原式=∫(-π/6,π/6)cosΘ*cosΘdΘ=∫(-π/6,π/6)(1+cos2Θ)/2*1/2d(2Θ)=1/4*(sin2Θ+2Θ)|(-π/6,π/6)=√3/4+π/6
Sqrt[3]/4 + \[Pi]/6