# 
restart;
F:=x->-1/(2*(x^2+9))
      +1/(2*3^3)*(3*x/(x^2+9)+arctan(x/3));
f:=D(F);
simplify(f(x));
V:=Int((x+1)/(x^2+9)^2,x);
V2:=value(V);
F2:=unapply(V2,x);
plot([F(x),F2(x)+0.01],x=-5..5);
plot(F(x)-F2(x),x=-5..5);
Digits:=60;
plot(F(x)-F2(x),x=-5..5);

#