Найдите первообразнуюf(x)=cos2x/cosx-sinx

Question

Найдите первообразную
f(x)=cos2x/cosx-sinx

Answer 1

F(x)=cos2x/(cosx-sinx)=(cosx-sinx)(cosx+cosx)/(cosx-sinx)=cosx+sinx=sin(π/2-x)+sinx=
=2sinπ/4cos(π/4-x)=√2cos(π/4-x)
F(x)=-√2sin(π/4-x)*(-1)+C=√2sin(π/4-x)+C