• # question_answer $\int{\sqrt{x-3}\,({{\sin }^{-1}}\ell nx+{{\cos }^{-1}}\ell n\,x)}\,\,dx$ is equal to A) $\frac{\pi }{3}{{(x-3)}^{3/2}}+c$ B) 0 C) does not exist     D) none of these

 $\because$       $x>3$ So $\ell n\,x>\ell n\,3>1$ So ${{\sin }^{-1}}\,(\ell n\,x)$ & ${{\cos }^{-1}}\ell n\,x$ are not define. Hence the given integral does not exist.