Solveeit Logo
Login

Question

Question: \[\int_{}^{}{\mathbf{\cos}^{\mathbf{-}\mathbf{1}}\left( \frac{\mathbf{1}}{\mathbf{x}} \right)}\mathb...

∫cos⁡−1(1x)dx=\int_{}^{}{\mathbf{\cos}^{\mathbf{-}\mathbf{1}}\left( \frac{\mathbf{1}}{\mathbf{x}} \right)}\mathbf{dx =}

A

xsec⁡−1x+cos⁡h−1x+cx\sec^{- 1}x + \cos h^{- 1}x + c

B

xsec⁡−1x−cos⁡h−1x+cx\sec^{- 1}x - \cos h^{- 1}x + c

C

cos⁡h−1x−xsec⁡−1x+c\cos h^{- 1}x - x\sec^{- 1}x + c

D

None of these

Answer

xsec⁡−1x−cos⁡h−1x+cx\sec^{- 1}x - \cos h^{- 1}x + c

Explanation

Solution

∫cos⁡−1(1x)dx=∫sec⁡−1xdx\int \cos ^ { - 1 } \left( \frac { 1 } { x } \right) d x = \int \sec ^ { - 1 } x d x

=xsec⁡−1x−∫1xx2−1xdx= x \sec ^ { - 1 } x - \int \frac { 1 } { x \sqrt { x ^ { 2 } - 1 } } x d x =xsec⁡−1x−cos⁡h−1x+c.= x\sec^{- 1}x - \cos h^{- 1}x + c.