alpha_sum :=
proc(n)
local poles;

    poles :=
    [[1+I, 1/2*log(2) + I*Pi/4],
     [1-I, 1/2*log(2) + 7*I*Pi/4],
     [-2, log(2) + I*Pi]];

    add(residue(1/(x^3-2*x+4), x=p[1])*p[2]^n,
                p in poles);
end;

Q :=
proc(n)
option remember;
    local res;

    if n = 0 then
        return
        simplify(int(1/(x^3-2*x+4), x=0..infinity));
    fi;

    res :=
    -1/(n+1)*alpha_sum(n+1)
    -1/(n+1)*add(binomial(n+1, p)*(2*Pi*I)^(n-p)*Q(p),
                 p=0..n-1);

    simplify(res);
end;

VERIF := n -> int((log(x))^n/(x^3-2*x+4), x=0..infinity);