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$\int \frac{\cos e c^{2} x - 2005}{\cos^{2005} x} d x$

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cotxcosx2005+C

tanxcosx2005+C

tanxcotx2005+C

−cotxcosx2005+C

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detailed solution

Correct option is D

I=∫(cos⁡x)−2005cos⁡ec2xdx−2005∫dxcos2005⁡xI=(cos⁡x)−2005(−cot⁡x)−∫(−2005)(cos⁡x)−2006(−sin⁡x)(−cot⁡x)dx−2005∫dxcos2005⁡xI=-cot⁡x(cos⁡x)2005+C

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∫cosec2x−2005cos2005xdx

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$\int \frac{\cos e c^{2} x - 2005}{\cos^{2005} x} d x$