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$\int \sqrt{\frac{\cos x - \cos^{3} x}{1 - \cos^{3} x}} d x is equal to$

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23sin−1⁡cos3/2⁡x+C

32sin−1⁡cos3/2⁡x+C

23cos−1⁡cos3/2⁡x+C

None of these

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detailed solution

Correct option is C

∫cos⁡x−cos3⁡x1−cos3⁡xdx=∫cos⁡x1−cos3⁡xsin⁡xdx=∫t1−t3dt=−∫t1−t3/22dt, where t=cos⁡x=−23∫32t1−t3/22dt=23cos−1⁡t3/2+C=23cos−1⁡(cos⁡x)3/2+C

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∫cos⁡x−cos3⁡x1−cos3⁡xdx is equal to

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$\int \sqrt{\frac{\cos x - \cos^{3} x}{1 - \cos^{3} x}} d x is equal to$