If $\int_{-\pi / 2}^{\pi / 2} \frac{8 \sqrt{2} \cos x d x}{\left(1+e^{\sin x}\right)\left(1+\sin ^4 x\right)}=\alpha \pi+\beta \log _e(3+2 \sqrt{2})$, where $\alpha, \beta$ are integers, then $\alpha^2+\beta^2$ equals
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