Example 3. Find the integral $\int\left(1-\frac{1}{x^{2}}\right)^{2} d x$.
Solution. Expanding the brackets and using formula (4.5) for the case when $m$ is a negative number, we find

$$
\begin{aligned}
& \int\left(1-\frac{1}{x^{2}}\right)^{2} d x=\int\left(1-\frac{2}{x^{2}}+\frac{1}{x^{4}}\right) d x=\int d x-2 \int \frac{d x}{x^{2}}+\int \frac{d x}{x^{4}}= \\
& =\int d x-2 \int x^{-2} d x+\int x^{-4} d x=x-2 \frac{x^{-2+1}}{-2+1}+\frac{x^{-4+1}}{-4+1}+C= \\
& =x+2 x^{-1}-\frac{1}{3} x^{-3}+C=x+\frac{2}{x}-\frac{1}{3 x^{3}}+C
\end{aligned}
$$