\[\alpha\ln\left(\left(\alpha^{2}+\eta^{2}\right)^{1/2}+\alpha\right)-\alpha\ln%
\eta-\left(\alpha^{2}+\eta^{2}\right)^{1/2}=\frac{1}{2}\ln\left(\frac{\left(1+%
\alpha^{2}\right)x^{2}+1-\alpha^{2}-2x\left(\alpha^{2}x^{2}-\alpha^{2}+1\right%
)^{1/2}}{\left(x^{2}-1\right)\left(1-\alpha^{2}\right)}\right)+\frac{1}{2}%
\alpha\ln\left(\frac{\alpha^{2}\left(2x^{2}-1\right)+1+2\alpha x\left(\alpha^{%
2}x^{2}-\alpha^{2}+1\right)^{1/2}}{1-\alpha^{2}}\right).\]