Question

Evaluate $\int \frac{dx}{x\sqrt{3-{\ln }^{2}x}}$

Answer 1

let $t=\ln x$

$dt=\frac{1}{x}dx$

$\int \frac{dx}{x\sqrt{3-{\ln }^{2}x}}$

$=\int \frac{dt}{\sqrt{1-t^2}}$

$={\sin }^{-1}t+c$

$={\sin }^{-1}\left(\ln \right(x\left)\right)+c$