Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
\(\int \frac{\sin ^3(x)+\cos ^3(x)}{\sin ^2(x) \cdot \cos ^2(x)} d x=\)
MathematicsIndefinite IntegrationAP EAMCETAP EAMCET 2020 (21 Sep Shift 1)
Options:
  • A \(\sec (x)-\operatorname{cosec}(x)+c\)
  • B \(\tan (x)+\cot (x)+c\)
  • C \(\operatorname{cosec}(x)-\cot (x)+c\)
  • D \(\tan (x)-\cot (x)+c\)
Solution:
2909 Upvotes 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.

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.