Question

If $\int_{-\pi/2}^{\pi/2} \frac{8\sqrt{2} \cos x \, dx}{(1 + e^{\sin x})(1 + \sin^4 x)} = \alpha \pi + \beta \log_e(3 + 2\sqrt{2}),$ where $\alpha$ and $\beta$ are integers, then $\alpha^2 + \beta^2$ equals ____.

Answer 1

The correct answer is