On the interval $(-\infty,\infty)$ with weight function $e^{-x^{2}}$

$\langle -4x,x^{2}-5 \rangle =$

$\displaystyle\int$

$dx =$

$\Vert -4x\Vert=\Bigg($

$\displaystyle\int$

$dx\Bigg)^\frac{1}{2} =$