\[2\omega_{1}=\int_{e_{1}}^{\infty}\frac{\,\mathrm{d}u}{\sqrt{(u-e_{1})(u-e_{2})%
(u-e_{3})}}=\int_{e_{3}}^{e_{2}}\frac{\,\mathrm{d}u}{\sqrt{(e_{1}-u)(e_{2}-u)(%
u-e_{3})}},\]