令t=arccosx，则x=cost，dx=-sintdt
原式=∫(π/2,0) cos^2t*t/sint*(-sint)dt
=∫(0,π/2) tcos^2tdt
=(1/2)*∫(0,π/2) t(1+cos2t)dt
=(1/2)*∫(0,π/2) tdt+(1/2)*∫(0,π/2) tcos2tdt
=(1/4)*t^2|(0,π/2)+(1/4)*∫(0,π/2) td(sin2t)
=π^2/16+(1/4)*tsin2t|(0,π/2)-(1/4)*∫(0,π/2) sin2tdt
=π^2/16+(1/8)*cos2t|(0,π/2)
=(π^2)/16-1/4
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