Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 28

$$ \frac{-1}{4(x-9)^4}$$

Given $$ \int\frac{dx}{(x-9)^5} $$ Let $$ u= x-9\ \ \ \Rightarrow\ \ du= dx$$ Then \begin{align*} \int\frac{dx}{(x-9)^5} &=\int\frac{du}{u^5} \\ &=\frac{-1}{4u^4}\\ &= \frac{-1}{4(x-9)^4} \end{align*}