The function $f(x)=x e^{-x} \forall x \in R$ attains a maximum value at $x=k$, then $k=$

If $m$ and $M$ are the absolute minimum and absolute maximum values of the function $f(x)=2 \sqrt{2} \sin x-\tan x$ in the interval $[0, \pi / 3]$, then $m+M=$

$$ \int \frac{\sec ^2 x}{\sin ^7 x} d x-\int \frac{7}{\sin ^7 x} d x= $$