令x=cost则原式=∫(π/2→π/4)t/sin^3(t)*(-sint)dt=∫(π/4→π/2)t/sin^2(t)dt=-∫(π/4→π/2)td(cott)=-tcott|(π/4→π/2)+∫(π/4→π/2)cottdt=0+π/4-∫(π/4→π/2)d(sint)/sint=π/4-ln|sint||(π/4→π/...可以令x=sint吗也可以吧。不过我觉得arccos(sint)不太好化简，至少看着就有点别扭……