Chapter 8: Techniques of Integration - Section 8.6 - Integral Tables and Computer Algebra Systems - Exercises 8.6 - Page 481: 35

$\sinh^{-1}(\dfrac{\ln y}{\sqrt 3})+C$

Use the formula: $\int\dfrac{dx}{\sqrt{a^2+x^2}}=\sinh^{-1}\dfrac{x}{a}+C $. Let $I=\int\dfrac{dy}{y\sqrt{3+(\ln y)^2}} $ Suppose $u=\ln y \implies du=\dfrac{dy}{y}$ Therefore, $I=\int\dfrac{du}{\sqrt{3+u^2}}=\sinh^{-1} (\dfrac{\ln y}{\sqrt{3}})+C$