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$\int \frac{{cosec}^{2} x - 2005}{\cos^{2005} x} dx$

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cot ⁡x(cos⁡ x)2005+C

tan ⁡x(cos ⁡x)2005+

−tan⁡ x(cos ⁡x)2005+C

−cot ⁡x(cos ⁡x)2005+C

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detailed solution

Correct option is D

I=∫(cos ⁡x)−2005cosec2⁡ x dx−2005∫dxcos2005 ⁡xI=(cos ⁡x)−2005(−cot⁡x)−∫(−2005)(cos ⁡x)−2006 (−sin ⁡x)(−cot⁡x)dx−2005∫dxcos2005⁡ x I=−cot ⁡x(cos⁡ x)2005+C

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∫cosec2 ⁡x−2005cos2005⁡ xdx

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$\int \frac{{cosec}^{2} x - 2005}{\cos^{2005} x} dx$