restart;
F:=ln(abs(x+1))-ln(abs(x+2));
plot(F,x=-4..4,y=-4..4);
?piecewise
C:=piecewise(x>-1,3,
             x>-2 and x<-1,1,
             x<-2,4);

plot(F+C,x=-4..4,y=-8..8);
a1:=int((B*x+E)/(x^2+x+1),x);
t2:=op(3,op(2,a1));
collect(a1,t2);