∫1/(sinx+cosx) dx
=∫1/[√2·(sinxcosπ/4+sinπ/4·cosx)]dx
=∫1/[√2·sin(x+π/4)] dx
=√2/2 ∫csc(x+π/4) d(x+π/4)
=√2/2 ln|csc(x+π/4)-cot(x+π/4)|+C