∫dx/sin2x+2sinx
=∫dx/2sinx(cosx+1)
=∫dx/8sin(x/2)cos(x/2){cox(x/2)}^2
=1/4∫1/sin(x/2)cos(x/2)dtan(x/2)
=1/4∫(cos(x/2)/sin(x/2)+sin(x/2)/cos(x/2)dtan(x/2)
=1/4∫1/tan(x/2)dtan(x/2)+1/4∫tan(x/2)dtan(x/2)
=1/4ln绝对值tan(x/2)+1/8{tan(x/2)}^2+C
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