( α 2 + η ) 1 / 2 + 1 2 ⁢ α ⁢ ln ⁡ η − α ⁢ ln ⁡ ( ( α 2 + η ) 1 / 2 + α ) = arccos ⁡ ( 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)}