If
$$\alpha = \int _ { 0 } ^ { 1 } \left( e ^ { 9 x + 3 \tan ^ { - 1 } x } \right) \left( \frac { 12 + 9 x ^ { 2 } } { 1 + x ^ { 2 } } \right) d x$$
where $\tan ^ { - 1 } x$ takes only principal values, then the value of $\left( \log _ { e } | 1 + \alpha | - \frac { 3 \pi } { 4 } \right)$ is