Assuming you mean dy/dx = (3x + y + 4)^2
Let v = 3x + y + 4
giving, dy/dx = v^2, and dv/dx = 3 + dy/dx
Therefore, dv/dx = 3 + v^2
rearranging as, dv/(3+v^2) = dx (here is where the variables are separated)
or, dv/(1 + (v/rt(3))^2) = 3dx (to be on their own side of the equal sign)
integrating both sides,
rt(3).tan^(-1)(v/rt(3)) = 3x + C
tan^(-1)((3x+y+4)/rt(3)) = 3.rt(3)x + C2
3x + y + 4 = rt(3).tan(3.rt(3).x + C2)