I'm trying to write $\int\frac{1-\cos x}{x}dx$ as power series. I know that
$\cos x=\sum_{k=0}^{\infty}\frac{(-1)^{k}x^{2k}}{(2k)!}$, so $\frac{1-\cos x}{x}$ should be $\frac{1-\cos x}{x}=\sum_{k=1}^{\infty}\frac{(-1)^{k+1}x^{2k-1}}{(2k)!}$, but this is just function under the integral. I don't understand how to write integral as power series, not only the funktion under the integral. Can anyone help me?