f\left( x \right) - \frac{{s_1 x^1 }}{{1!}} - \frac{{s_0 x^0 }}{{0!}} = \int {\frac{d}{{dx}}\left( {\sum\limits_{n \ge 2} {\frac{{s_{n - 1} x^n }}{{n!}}} } \right)dx} + \int {\frac{d}{{dx}}\left( {\sum\limits_{n \ge 2} {\frac{{\left( {n - 1} \right)s_{n - 2} x^n }}{{n!}}} } \right)dx}