( α 2 + η ) 1 / 2 + 1 2 α ln η − α ln ( ( α 2 + η ) 1 / 2 + α ) = a r c c o s ( x ( 1 + α 2 ) 1 / 2 ) + α 2 ln ( 1 + α 2 + ( α 2 − 1 ) x 2 − 2 α x ( 1 + α 2 − x 2 ) 1 / 2 ( 1 + α 2 ) ( 1 − x 2 ) ) {\left(\alpha^{2}+\eta\right)^{1/2}+\tfrac{1}{2}\alpha\ln\eta-\alpha\ln\left(\left(\alpha^{2}+\eta\right)^{1/2}+\alpha\right)}={\operatorname{arccos}\left(\frac{x}{\left(1+\alpha^{2}\right)^{1/2}}\right)+\frac{\alpha}{2}\ln\left(\frac{1+\alpha^{2}+\left(\alpha^{2}-1\right)x^{2}-2\alpha x\left(1+\alpha^{2}-x^{2}\right)^{1/2}}{\left(1+\alpha^{2}\right)\left(1-x^{2}\right)}\right)}