In order to evaluate the inclusive decay rate $H \to VV^* \to Vf\overline{f}$ (i.e the Higgs decays into an on-shell vector boson and two fermions via an off-shell vector boson), one needs to compute the following integral:
$$\int_{2\epsilon}^{1 + \epsilon^2}\!\mathrm{d}x\,\frac{(x^2 - 4\varepsilon^2)^{1/2}}{(1 - x)^2}(x^2 - 12\varepsilon^2x + 8\varepsilon^2 + 12\varepsilon^4)$$
where $\varepsilon = \frac{M_V}{M_H}$. The claimed result, stated in this paper, equations 6, 8a and 8b is:
$$\frac{3(1 - 8\varepsilon^2 + 20\varepsilon^4)}{(4\varepsilon^2 - 1)^{1/2}}\arccos\left(\frac{3\varepsilon^2 - 1}{2\varepsilon^3}\right) - (1 - \varepsilon^2)\left(\frac{47}{2}\varepsilon^2 - \frac{13}{2} + \frac{1}{\varepsilon^2}\right) - 3(1 - 6\varepsilon^2 + 4\varepsilon^4)\ln\varepsilon$$
but no further details are given. Any idea where this result stems from?