\int\frac{2(\alpha-\beta)dz}{\sqrt{-(z^2(a\alpha + b + \alpha^2) + z(a(\alpha + \beta) + 2(b + \alpha\beta)) + a\beta + b + \beta^2)(z^2(a\alpha - b - \alpha^2) + z(a(\alpha + \beta) - 2(b + \alpha\beta)) + a\beta - b - \beta^2)}