I need to solve the following integral:
$$x\int\frac{e^{\frac{-x^2}{2}}}{x^2}\,dx$$
I'm told that by using the Taylor expansion of $e^z$ and "integrating term by term" show that it's equal to:
$$\alpha x + \sum_{n=0}^{\infty}\frac{(-1)^n}{2^n(2n-1)n!}x^{2n}.$$
Really not sure what to do.