Integrating factor is e^∫dx/x=e^ln(x)=x.
So the integrating factor x simply returns the DE to its original form!
That means x(dy/dx)+y=d(xy)/dx.
Integrate by parts u=x, du=dx, dv=sin(x)dx, v=-cos(x).
y=-cos(x)+(sin(x)+C)/x. C is a constant of integration.
The DE appears to use integration by parts rather than an integrating factor.