Answer
$(\dfrac{-1}{2}) \ln |9-x^2|+c$
Work Step by Step
Consider the integral $\int \dfrac{x dx}{9-x^2}$
The given integral can be re-written as: $\int \dfrac{x dx}{9-x^2}=(\dfrac{-1}{2})\int\dfrac{-2x dx}{(9-x^2)}$
This implies that $(\dfrac{-1}{2})\int\dfrac{-2x dx}{(9-x^2)}=(\dfrac{-1}{2}) \ln |9-x^2|+c$
