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}