1. The problem is to simplify or integrate an expression using the substitution $u=9-x^2$. 2. The substitution method involves replacing a complicated expression with a simpler variable to make the problem easier. 3. Given $u=9-x^2$, differentiate both sides with respect to $x$ to find $du$: $$du = -2x\,dx$$ 4. Rearranging for $dx$ gives: $$dx = \frac{du}{-2x}$$ 5. Substitute $u$ and $dx$ into the original expression (not provided, but typically an integral involving $9-x^2$) to simplify. 6. Use the substitution to rewrite the integral or expression entirely in terms of $u$ and $du$. 7. Solve the simplified problem in $u$, then substitute back $u=9-x^2$ to get the final answer. Since the original expression or integral is not specified, this is the general substitution process for $u=9-x^2$.