Let \( \int x^3 \sin x \, dx = g(x) + C \), where \( C \) is the constant of integration.
If \(\displaystyle 8\Big(g\!\left(\frac{\pi}{2}\right) + g'\!\left(\frac{\pi}{2}\right)\Big) = \alpha \pi^3 + \beta \pi^2 + \gamma, \, \alpha,\beta,\gamma \in \mathbb{Z} \), then \( \alpha + \beta - \gamma \) equals:
