If ∫_-π / 2^π / 2 (8 √ 2 cos x d x)/((1+e^sin x)(1+ sin^4 x))=α π+β log_e(3+2 √ 2 ), where α, β are integers, then α^2+β^2 equals ____.

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