∫$$cos$$−$$1$$⁡$$1xdx$$ is equal to

Correct option is 2xsec−1⁡x−cosh−1⁡x+C

Questions

$\int \cos^{- 1} (\frac{1}{x}) dx$ is equal to

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xsec−1⁡x+cosh−1⁡x+C

xsec−1⁡x−cosh−1⁡x+C

xsec−1⁡x−sin−1⁡x+C

None of the above

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detailed solution

Correct option is B

∫cos−1⁡1xdx=∫sec−1⁡x⋅1dx=sec−1⁡x∫dx−∫ddxsec−1⁡x∫dxdx=xsec−1⁡x−∫1xx2−1xdx=xsec−1⁡x−∫1x2−1dx=xsec−1⁡x−cosh−1⁡x+C

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∫cos−1⁡1xdx is equal to

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$\int \cos^{- 1} (\frac{1}{x}) dx$ is equal to