$$S=$$∫[$$cot$$⁡(log$$⁡$$x)]$$5cosec2$$⁡(log$$⁡$$x)xdx(x$$>$$0) is equal to

Correct option is 2−16cotlogx6+C

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$S = \int \frac{[\cot (\log x)]^{5} {cosec}^{2} (\log x)}{x} d x (x > 0) is equal to$

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112cotlogx12+C

−16cotlogx6+C

−16cotx6

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detailed solution

Correct option is B

S=∫cot(logx)5cosec2(logx)xdxlog⁡x=y1xdx=dyS=∫(cot⁡y)5cos⁡ec2(y)dy Put cot⁡y=zcos⁡ec2ydy=−dzS=∫z5(−dz)=−z66+C=−16(cot⁡y)6+CS=−16(cot⁡(log⁡x))6+C

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S=∫[cot⁡(log⁡x)]5cosec2⁡(log⁡x)xdx(x>0) is equal to

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$S = \int \frac{[\cot (\log x)]^{5} {cosec}^{2} (\log x)}{x} d x (x > 0) is equal to$