For real numbers \( \alpha, \beta, \gamma \) and \( \delta \), if
\( \int \dfrac{(x^{2}-1) + \tan^{-1}\!\left(\dfrac{x^{2}+1}{x}\right)}{(x^{4}+3x^{2}+1)\,\tan^{-1}\!\left(\dfrac{x^{2}+1}{x}\right)} \, dx = \alpha \log_{e}\!\left( \tan^{-1}\!\left(\dfrac{x^{2}+1}{x}\right) \right) + \beta \tan^{-1}\!\left( \dfrac{\gamma (x^{2}-1)}{x} \right) + \delta \tan^{-1}\!\left( \dfrac{x^{2}+1}{x} \right) + C \) where \( C \) is an arbitrary constant, then the value of \( 10(\alpha+\beta\gamma+\delta) \) is equal to ________.
