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$\int \sqrt{x - 3} \{\sin^{- 1} (\ln x) + \cos^{- 1} (\ln x)\} d x$ is equal to

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\frac{π}{3} (x - 3)^{3 / 2} + C

does not exist

none of these

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detailed solution

Correct option is C

We know that

$\sin^{- 1} x + \cos^{- 1} x = \frac{π}{2},$ if $- 1 \leq x \leq 1$

Since, $\ln x \in (- \infty, \infty) .$ Therefore,

$\sin^{- 1} (\ln x) + \cos^{- 1} (\ln x)$ does not exist.

Hence, the given integral does not exist.

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∫x−3sin−1⁡(ln⁡x)+cos−1⁡(ln⁡x)dx is equal to