How to expand $x^n$ as $n \to 0$? I am trying to expand $x^n$ in small $n$ using Taylor series.
Using wolfram alpha, I found that it is $1+ n\log(x) + \cdots$
I tried to Taylor expand $x^n$ around $n=0$ but I cannot get this result. 

Hint. One may recall that
$$
e^z=1+z+\cdots+\frac{z^k}{k!}+\cdots,\quad z \in \mathbb{C},
$$ then, for $x>0$ and for $0<n<1$,
$$
\begin{align}
x^n&=e^{n\ln x}=1+n\ln x+\frac{n^2(\ln x)^2}{2!}+\cdots+\frac{n^k(\ln x)^k}{k!}+\cdots,
\\\\x^n&=1+n\ln x+\cdots+\mathcal{O}\left(n^k\right),
\end{align}
$$ as announced.
