Determine the antiderivative of $f(x)=1/x^3$.

We can use Antiderivative Rule 4 to solve this. But before we do we need to cast the problem differently. Remember,
$$f(x)=\frac{1}{x^3}=x^{-3}.$$
Now we can apply the rule:
$$\begin{eqnarray} F(x)&=&\frac{1}{-3+1}x^{-3+1}\\ &=&-\frac{1}{2}x^{-2}\\ &=&-\frac{1}{2x^2} \end{eqnarray}$$