Chapter 8 - Techniques of Integration - 8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions - Exercises - Page 415: 20

$$\frac{1}{3} \sinh ^{-1}(\sqrt{3} x)+C$$

\begin{aligned} \int \frac{1}{\sqrt{1+3 x^{2}}} d x &=\frac{1}{\sqrt{3}} \int \frac{\sqrt{3}}{\sqrt{1+(\sqrt{3} x)^{2}}} d x \\ &=\frac{1}{3} \sinh ^{-1}(\sqrt{3} x)+C \end{aligned}