In this paper we prove that \[ im_{noıfty}ıt^T_0\Big(\frac{n+1}t\Big)^{n+1}R^{n+1}\Big(\frac{n+1}t;A\Big)dt=S(T),\quad T>0 \] where $S(T)$ is one-time integrated exponentially bounded semigroup and limit is uniform in $T>0$ on any bounded interval.