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$\int \sin^{- 7 / 5} {xcos}^{- 3 / 5} dx$ is equal to

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−25(tan⁡x)2/5+C

−52(cot⁡x)2/5+C

−52(tan⁡x)2/5+C

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detailed solution

Correct option is B

Here, p=−75,q=−35p+q=−2I=∫sin−7/5⁡xcos−3/5⁡xdx=∫cos−3/5⁡xsin−3/5⁡xsin2⁡xdx=∫(cot⁡x)−3/5cosec2⁡xdxPut, cot⁡x=t⇒cosec2⁡xdx=−dtSo, I=−∫t−3/5dt=−52(cot⁡x)2/5+C

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∫sin−7/5⁡xcos−3/5⁡dx is equal to

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$\int \sin^{- 7 / 5} {xcos}^{- 3 / 5} dx$ is equal to