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$\int \frac{\sin^{4} x}{\cos^{2} x} d x is equal to$

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−3x2+14sin⁡2x−2tan⁡x+C

−3x2−14sin⁡2x+tan⁡x+C

−3x2+14sin⁡2x+tan⁡x+C

−3x2−14sin⁡2x−2tan⁡x+C

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detailed solution

Correct option is C

I=∫sin4⁡xcos2⁡xdx=∫sec2⁡x1−cos2⁡x2dx=∫sec2⁡x1+cos4⁡x−2cos2⁡xdx=∫sec2⁡x+cos2⁡x−2dx=∫sec2⁡x+1+cos⁡2x2−2dx=∫−32+12cos⁡2x+sec2⁡xdx=−32x+14sin⁡2x+tan⁡x+C

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∫sin4⁡xcos2⁡xdx is equal to

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$\int \frac{\sin^{4} x}{\cos^{2} x} d x is equal to$