令x=tant
原式=∫(0→π/2)tcos^3(t)/cos^2(t)dt=∫(0→π/2)tcostdt=∫(0→π/2)td(sint)=tsint|(0→π/2)-∫(0→π/2)sintdt=tsint|(0→π/2)+cost|(0→π/2)=π/2-1请问那个arctanx你化到哪里去了哦？能写的清楚点吗，谢谢，感觉有点小乱~~~arctan(tant)=t(1+x^2)^(1/2)=(1/cos^2t)^(1/2)=1/costx从0到+∞就是t从0到π/2我懂了，谢谢啊~~~