Give an example of a power series expansion of a rational function whose antiderivative is not the expansion of a rational function.
(The antiderivative of a power series $f(x) = \sum_{n=0}^{\infty} c_n x^n$ is defined as $\int_0^x f(t)\,dt \stackrel{\text{def}}{=} \sum_{n=0}^{\infty} \frac{c_n}{n+1} x^{n+1}$.)