Example 7. Find the integral $\int \frac{d x}{\sin ^{2} x \cos ^{2} x}$.
Solution.

$$
\begin{gathered}
\int \frac{d x}{\sin ^{2} x \cos ^{2} x}=\int \frac{\cos ^{2} x+\sin ^{2} x}{\sin ^{2} x \cdot \cos ^{2} x} d x=\int \frac{d x}{\sin ^{2} x}+\int \frac{d x}{\cos ^{2} x}= \\
=-\operatorname{ctg} x+\operatorname{tg} x+C
\end{gathered}
$$