\int{\frac{\sin x}{x}}dx=\int{\sum_{n=0}^\infty(-1)^n\frac{x^{2n}}{(2n+1)!}}dx=\sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)!}\int{x^{2n}}dx=\sum_{n=0}^\infty(-1)^n\frac{x^{2n+1}+C}{(2n+1)(2n+1)!}