Finding the function with power series $ \sum_{n=1}^{\infty} \frac{(-1)^{n+1} x^n}{n^2}$

I want to evaluate the power series $$ f(x) = \sum_{n=1}^{\infty} \frac{(-1)^{n+1} x^n}{n^2}. $$I am getting that $f(x)$ is equal to some integral of $\dfrac{\ln(x+1)}x$, which is not elementary integrable.

I don't get it. Did I make a mistake? Or is it that the power series can not be written as a composition of elementary functions on some interval.