∫secxdx=∫dx/cosx=∫cosxdx/(cosx)^2=∫d(sinx)/[1-(sinx)^2],以u=sinx作代换=∫du/(1-u^2)=0.5∫du[1/(1-u)+1/(1+u)]=0.5ln|(1+u)/(1-u)|+C=0.5ln|(1+sinx)/(1-sinx)|+C=ln|(1+sinx)/cosx|+C