高数∫1/(1+secx) dx要详细过程

网友回答

设tan(x/2)=u
x=2arctanu
dx=2du/1+u^2
cosx=1-u^2/1+u^2
积分=∫cosx/1+cosx dx=∫(1-u^2)/(1+u^2) dt=∫2/(1+u^2) -1
=-u+2arctanu+C
代入u=-tan(x/2)+2x+C