Intergreeting Integrals #3

$\sqrt{x-3}$ is defined only when $x\ge{3}$ and $sin^{-1}(ln x)$ and $cos^{-1}(ln x)$ is defined only when $-1\le{ln x}\le{1}$ which implies $\dfrac{1}{e}\le{x}\le{3}$ Then, $[3,\infty)\cup[\dfrac{1}{e},e]=\phi$ .Hence the given integral does not exist...