What is the general solution for integrals of the form $\int\frac{\;\ln^{m}(x+n) }{(x+n)^{b}e^{\alpha (x+n)}} dx$?

Question

I have this integral $$\int\frac{\;\ln^{m}(x+n) }{(x+n)^{a}e^{\alpha (x+n)}} dx;\;\;m,n\in\mathbb{N_{>0}};\;\;a\in\mathbb{Q};\;\;\alpha\in\mathbb{R_{>0}}$$ I've tried to solve it with Wolframalpha but with no luck.

I'm looking for solutions based on simple functions like those entering in the integral, i.e. $\ln(x+n),\;(x+n)$, etc.

Any help would be very much apreciated.

Thanks in advance.

Answer 1

Don't think there is one, especially as the case $m=0$, $a=1$, $\alpha = 1$ corresponds to the integral $\int \frac{e^{-(x+n)}}{x+n}\, {\rm d} x$ or, after a linear switch of variables, $\int \frac{e^{-v}}{v}\, {\rm d}v$; the latter integral is classically irreducible (see this page).