For real numbers α, β, γ and δ, if ∫ ((x^2-1)+ tan^-1((x^2+1)/x))/((x^4+3 x^2+1) tan^-1((x^2+1)/x)) d x = α log_e( tan^-1((x^2+1)/x))+β…

For real numbers $\displaystyle \alpha, \beta, \gamma$ and $\displaystyle \delta$, if $$\begin{aligned} & \int \frac{\left(x^2-1\right)+\tan ^{-1}\left(\dfrac{x^2+1}{x}\right)}{\left(x^4+3 x^2+1\right) \tan ^{-1}\left(\dfrac{x^2+1}{x}\right)} d x \\ = & \alpha \log _e\left(\tan ^{-1}\left(\frac{x^2+1}{x}\right)\right)+\beta \tan ^{-1}\left(\frac{\gamma\left(x^2-1\right)}{x}\right)+\delta \tan ^{-1}\left(\frac{x^2+1}{x}\right)+C \end{aligned} $$ where $\displaystyle C$ is an arbitrary constant, then the value of $\displaystyle 10(\alpha+\beta \gamma+\delta)$ is equal to \_\_\_\_.