Let $\alpha$ and $\beta$ be the real numbers such that
$$\lim _ { x \rightarrow 0 } \frac { 1 } { x ^ { 3 } } \left( \frac { \alpha } { 2 } \int _ { 0 } ^ { x } \frac { 1 } { 1 - t ^ { 2 } } d t + \beta x \cos x \right) = 2$$
Then the value of $\alpha + \beta$ is $\_\_\_\_$ .