Answer
$-\displaystyle \frac{(-x-1)^{8}}{8}+C$
Work Step by Step
see Substitution RuIe, p.962:
(1)
let $u=-x-1$
(2)
$du=-dx\ \ \Rightarrow\ \ dx=-du$
$(3)$
$\displaystyle \int(-x-1)^{7}dx=\int u^{7}(-du)$
... constant multiple, power rules
$=-\displaystyle \frac{u^{8}}{8}+C$= ... bring back x
$=-\displaystyle \frac{(-x-1)^{8}}{8}+C$
