General antiderivative of a sum of two standard forms

The function $g(x)$ is a sum of two terms, so we can antidifferentiate each term separately using linearity. For the first term, recall that $\frac{d}{dx}[\arcsin x] = \frac{1}{\sqrt{1-x^2}}$, so an antiderivative of $\frac{1}{\sqrt{1-x^2}}$ is $\arcsin x$.

For the second term, recall that $\frac{d}{dx}[\arctan x] = \frac{1}{1+x^2}$, so an antiderivative of $\frac{3}{1+x^2}$ is $3\arctan x$. Adding these pieces together and including a single arbitrary constant of integration gives the general antiderivative $G(x) = \arcsin x + 3\arctan x + C$.