Integration solution needed with rational powers of $x$

Question

I want to solve the following integration $$\int_{0}^{\infty}\frac{x^{n/2}e^{-x}}{(x-1)^{m}}dx$$ where $n,m$ are positive integers. I can solve this integral if the limits are from $0 \to 1$ but I am unable to solve it for $0\to \infty$. I will be thankful to you for your help.

Answer 1

This is not an answer but a result a CAS produced.$$\int_{0}^{\infty}\frac{x^{n/2}e^{-x}}{(x-1)^{m}}dx=\, _1F_1\left(m;m-\frac{n}{2};-1\right) \Gamma \left(-m+\frac{n}{2}+1\right)-\frac{\pi (-1)^{-m} \Gamma (1-m) \, _1F_1\left(\frac{n}{2}+1;-m+\frac{n}{2}+2;-1\right) \left((-1)^m \csc \left(\pi m-\frac{\pi n}{2}\right)+\csc \left(\frac{\pi n}{2}\right)\right)}{\Gamma \left(-\frac{n}{2}\right) \Gamma \left(-m+\frac{n}{2}+2\right)}$$ But, take care : this is valid for $\Re(n)>-2\land \Re(m)<1$