∫1/(cos X+sin X)dx
=∫1/2^(1/2)sin(x+π/4)dx
=∫1/2^(1/2)sin(x+π/4)d(x+π/4)
=∫1/2^(1/2)2sin(x+π/4）/2cos(x+π/4）/2dx
=∫1/2^(1/2)lnItan(x+π/4）/2I+C