$\int \sqrt{x-3}\left\{\sin ^{-1}(\ln x)+\cos ^{-1}(\ln x)\right\} d x$ is equal to
Answer & explanation
Correct answer: option 3
We know that
$\sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}, \text { if }-1 \leq x \leq 1$
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.