Indefinite Integration

If $\int \frac{1}{x^{4}+8 x^{2}+9} d x=\frac{1}{k}$$\left[\frac{1}{\sqrt{14}} \tan ^{-1}(f(x))-\frac{1}{\sqrt{2}} \tan ^{-1}(g(x))\right]+c$ then,

$\sqrt{\frac{k}{2}+f(\sqrt{3})+g(1)}=$