List of practice Questions

Let $ \alpha $ and $ \beta $ be the real numbers such that $$ \lim_{x \to 0} \frac{1}{x^3} \left( \frac{\alpha}{2} \int_{0}^{x} \frac{1}{1 - t^2} \, dt + \beta x \cos x \right) = 2. $$ Then the value of $ \alpha + \beta $ is __________.