Find the integral of the function $\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}$.

(A) We are given the integral $I = \int \frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x} dx$.
First,simplify the integrand:
$\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x} = \frac{\sin ^{3} x}{\sin ^{2} x \cos ^{2} x} + \frac{\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}$
$= \frac{\sin x}{\cos ^{2} x} + \frac{\cos x}{\sin ^{2} x}$
$= \tan x \sec x + \cot x \csc x$
Now,integrate each term:
$\int (\tan x \sec x + \cot x \csc x) dx = \int \tan x \sec x dx + \int \cot x \csc x dx$
$= \sec x - \csc x + C$,where $C$ is an arbitrary constant.