A simplification of a definite integral would be a numerical result!
In[214]:= F = N[Integrate[(x^4*Exp[x])/(Exp[x] - 1)^2, {x, 0, 44}]] Out[214]= 25.9758
@S M Blinder. Thank you. That's what I am looking for.
What simpler form of result are you expecting?
