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

$\frac{\pi}{3}(x-3)^{3 / 2}+C$ 0 does not exist none of these

does not exist

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.