\(\int \frac{\sin ^3(x)+\cos ^3(x)}{\sin ^2(x) \cdot \cos ^2(x)} d x=\)
\(\int \frac{\sin ^3(x)+\cos ^3(x)}{\sin ^2(x) \cdot \cos ^2(x)} d x=\)
\(\sec (x)-\operatorname{cosec}(x)+c\)
\(\tan (x)+\cot (x)+c\)
\(\operatorname{cosec}(x)-\cot (x)+c\)
\(\tan (x)-\cot (x)+c\)
Solution
\(\begin{aligned}
& \int \frac{\sin ^3 x+\cos ^3 x}{\sin ^2 x \cos ^2 x} d x \\
& =\int(\sec x \tan x+\cot x \operatorname{cosec} x) d x \\
& =\sec x-\operatorname{cosec} x+C \\
\end{aligned}\)
Hence, option (a) is correct.