求定积分∫x/(cosx)^2dx 从0积到π/3,∫x/(cosx)^2dx

Answer 1

此题用分部积分法
∫x/(cosx)^2dx
=∫x (secx)^2dx
=∫xd(tanx)
=xtanx-∫tanxdx
=xtanx+ln/cosx/
最后把积分上下限一代就得到答案了
注：∫tanxdx=∫sinx/cosx dx
=-∫d(cosx)/cosx
=-ln/cosx/+c