Questions

$\int \frac{1}{\cos^{2} x \sin^{4} x} d x =$

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cotx−2tanx−cot3x3+C

cotx+2tanx−cot3x3+c

cotx+2tanx+tan3x3+c

tanx−2cotx−cot3x3+c

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detailed solution

Correct option is D

I=∫1cos2xsin4xdx=∫sin2x+cos2x2cos2xsin4xdx=∫sin4⁡x+2sin2⁡xcos2⁡x+cos4⁡xcos2⁡xsin4⁡xdx=∫sec2⁡x+2cosec2⁡x+cot2⁡xcosec2⁡x=tan⁡x−2cot⁡x−cot3⁡x3+c

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