∫secx(cscx)^2dx

∫secx(cscx)^2dx
∫secx(cscx)^2dx

∫secx(cscx)^2dx
secx(cscx)^2化为cosx/[cosx^2*sinx^2]
再化为cosx/[(1-sinx^2)sinx^2]
=cosx*[1/(1-sinx^2)+1/sinx^2]
则∫secx(cscx)^2dx=1/2ln|(1+sinx)/(1-sinx)|-1/sinx+C
=ln|tan(x/2+pi/4)|-1/sinx+C