Given that the first derivative of $f(x)$ is:

$f'(x) = \frac{x}{9 - x^4}$

To find $f(x)$, we need to integrate $f'(x)$ with respect to $x$.

Step 1: Set up the integral

$f(x) = \int \frac{x}{9 - x^4} \, dx$

Step 2: Simplify the integral

We notice that the denominator involves $x^4$, and the numerator is $x$. A substitution may help simplify the integral.

Let: $u = 9 - x^4$ Then, the derivative of $u$ with respect to $x$ is: $du = -4x^3 \, dx$ To match the $x$ term in the numerator, we need to isolate a single $x$, so rewrite $u$ as: [ f(x) = \int \frac{1}{9 - x^4} dx