设x=2t，则原式=∫(1+sin2t)/cos²tdt=∫1/cos²tdt+2∫sintcost/cos²tdt=tant+2∫sint/costdt=tant-2∫dcost/cost=tant-2lncost+C
=∫(1+sinx)(1-cosx)/sin²xdx=∫csc²x+cscx-cotxcscx-cotxdx=-cotx+ln|cscx-cotx|+cscx-ln|sinx|+C
