For real numbers α, β, γ and δ, if
\(\int \cfrac{x^2-1+tan^{-1}\bigg(\frac{x^2+1}{x}\bigg)}{(x^4+3x^2+1)tan^{-1}\bigg(\frac{x^2+1}{x}\bigg)}dx\)
\(=\alpha\,log_e \bigg(tan^{-1}\bigg(\frac{x^2+1}{x}\bigg)\bigg)\) \(+\,\beta\,tan^{-1}\bigg(\frac{\gamma(x^2-1)}{x}\bigg)\) \(+\,\delta\,tan^{-1}\bigg(\frac{x^2+1}{x}\bigg)+C\)
where C is an arbitrary constant, then the value of \(10(\alpha+\beta\gamma+\delta)\) is equal to __________.
