I don't understand the solution my textbook gives for this problem: $$ \int \! \frac{x^3}{(x+1)^5} \, \mathrm{d}x $$
I thought it had to be done with partial fractions, but I couldn't get it right, and when I checked the solution, it said "through Taylor's formula, you get:" $$ \frac{x^3}{(x+1)^5} = \frac{-1 + 3(x+1) - 3(x+1)^2 + (x+1)^3}{(x+1)^5} $$
Is there a Taylor's formula I don't know about? Or is this an use of Taylor's expansion I cannot see? Also, is there a general rule for this decomposition?
(I'm leaving here the textbook for reference, in case I mistranslated something)
Thank you in advance. This is really driving me mad.
(I apologize for any mistakes, English is not my first language)