> R:=x->6*C[1]*(x^2-x)+2*C[2]*(6*x^3-9*x^2+2*x)-6*x;

                        2                   3      2
     R := x -> 6 C[1] (x  - x) + 2 C[2] (6 x  - 9 x  + 2 x) - 6 x

> w[1]:=x->(x-1)*(x-2); w[2]:=x->(x-1)*(x-2)*x;

                     w[1] := x -> (x - 1) (x - 2)


                    w[2] := x -> (x - 1) (x - 2) x

> solve({int(w[1](x)*R(x),x=1..2)=0, int(w[2](x)*R(x),x=1..2)=0},
> {C[1],C[2]});

                              -231         711
                      {C[2] = ----, C[1] = ---}
                              179          179

> 
> 
