I have the following function defined piecewise continuous with $S,T\in\mathbb{R} > 0$
$$f(x)=\begin{cases} 
 \frac{e^{T/u}}{u^S} & x < 0 \\
 0 & x \geq 0 
 \end{cases}
$$

and I want to normalize this function to integrate to $1$. This creates a particularly tricky integral though that I have never seen before and I was wondering if anyone knew about how to get the value in terms of $S,T$

$$
\int\_{-\infty}^0 \frac{e^{T/x}}{x^S}dx
$$

I've tried the standard methods, but this appears harder then I'm used to, if anyone has some insight!