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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy
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Application +4 | -1
∫dxsin⁡5xcos⁡5x\int \frac{d x}{\sin ^5 x \cos ^5 x} is equal to
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Correct option: B
14(tan⁡4x−cot⁡4x)+2(tan⁡2x−cot⁡2x)+6log⁡∣tan⁡x∣\frac{1}{4}\left(\tan ^4 x-\cot ^4 x\right)+2\left(\tan ^2 x-\cot ^2 x\right)+6 \log |\tan x| +C+C
Option B is correct because the integral evaluates to 14(tan⁡4x−cot⁡4x)+2(tan⁡2x−cot⁡2x)+6log⁡∣tan⁡x∣+C\frac{1}{4}(\tan ^4 x-\cot ^4 x)+2(\tan ^2 x-\cot ^2 x)+6 \log |\tan x| +C after simplification.

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