AP EAMCET · Maths · Indefinite Integration
\(\int \frac{\sin ^3(x)+\cos ^3(x)}{\sin ^2(x) \cdot \cos ^2(x)} d x=\)
- A \(\sec (x)-\operatorname{cosec}(x)+c\)
- B \(\tan (x)+\cot (x)+c\)
- C \(\operatorname{cosec}(x)-\cot (x)+c\)
- D \(\tan (x)-\cot (x)+c\)
Answer & Solution
Correct Answer
(A) \(\sec (x)-\operatorname{cosec}(x)+c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \int \frac{\sin ^3 x+\cos ^3 x}{\sin ^2 x \cos ^2 x} d x \\ & =\int(\sec x \tan x+\cot x \operatorname{cosec} x) d x \\ & =\sec x-\operatorname{cosec} x+C \\ \end{aligned}\) Hence, option (a) is correct.
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