Example 7. Find the integral $\int \frac{d x}{\sin x \cos x}$.
Solution. Dividing the numerator and the denominator by $\cos ^{2} x$, we get

$$
\frac{1}{\sin x \cos x}=\frac{\frac{1}{\cos ^{2} x}}{\tan x}
$$

Let

$$
\tan x=t
$$

then

$$
\frac{1}{\cos ^{2} x} d x=d t
$$

Thus,

$$
\int \frac{d x}{\sin x \cos x}=\int \frac{\frac{d x}{\cos ^{2} x}}{\tan x}=\int \frac{d t}{t}=\ln |t|+C=\ln |\tan x|+C
$$