  The Moll-Arias de Reyna integral [1]
$$\int_0^{\infty}\frac{dx}{(x^2+1)^{3/2}}\frac{1}{\sqrt{\varphi(x)+\sqrt{\varphi(x)}}}$$
$$\varphi(x)=1+\frac{4}{3}\left(\frac{x}{x^2+1}\right)^2$$ is generalised and
several values are given.
