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If $\int \frac{1 - 5 \sin^{2} x}{\cos^{5} x \sin^{2} x} d x = \frac{f (x)}{\cos^{5} x} + C$ , then $f (x) :$

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-cosec x

cosec x

cot x

-cot x

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detailed solution

Correct option is D

∫1−5sin2⁡xcos5⁡xsin2⁡xdx=∫cosec2⁡xcos5⁡xdx−5∫1cos5⁡xdx=−cot⁡xcos5⁡x+∫cot⁡x−5cos−6⁡x(−sin⁡x)dx−5∫1cos5⁡xdx=−cot⁡xcos5⁡x+5∫dxcos5⁡x−5∫dxcos5⁡x+C=−cot⁡xcos5⁡x+CSo f(x)=-cotx

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If ∫1−5sin2⁡xcos5⁡xsin2⁡xdx=f(x)cos5⁡x+C, then f(x):

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Ready to Test Your Skills?

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If $\int \frac{1 - 5 \sin^{2} x}{\cos^{5} x \sin^{2} x} d x = \frac{f (x)}{\cos^{5} x} + C$ , then $f (x) :$