令x=tank,则k=arctanx,k的积分下限为0,上限为π/4(以下无上下限标注的均是这个值)原式=∫(1+x^)^(-3/2)dx=∫(1+tan^k)^(-3/2)d(tank)=∫(sec^k)^/(-3/2)*sec^k dk=∫(seck)^(-3) * sec^k dk=∫(seck)^(-1) dk=∫cosk...