令x=sint∫x^2/√(1-x^2)dx=∫sin²t/cost*costdt(上限π/6,下限0,下同)=∫sin²tdt=1/2∫(1-cos2t)dt=1/2*t-sin2t/4=1/2*(π/6-0)-(sinπ/3-sin0)/4=π/12-根号3/8=(2π-3根号3)/24