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