Question:
$\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}$
Solution:
$\frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}=\frac{\sin ^{3} x}{\sin ^{2} x \cos ^{2} x}+\frac{\cos ^{3} x}{\sin ^{2} x \cos ^{2} x}$
$=\frac{\sin x}{\cos ^{2} x}+\frac{\cos x}{\sin ^{2} x}$
$=\tan x \sec x+\cot x \operatorname{cosec} x$
$\begin{aligned} \therefore \int \frac{\sin ^{3} x+\cos ^{3} x}{\sin ^{2} x \cos ^{2} x} d x &=\int(\tan x \sec x+\cot x \operatorname{cosec} x) d x \\ &=\sec x-\operatorname{cosec} x+\mathrm{C} \end{aligned}$
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