The wavefunction of a 1 - D harmonic oscillator between $\mathrm{x}=+\infty$ and $\mathrm{x}=-\infty$ is given by $\psi(\mathrm{x})=\mathrm{N}\left(2 \mathrm{x}^{2}-1\right) \mathrm{e}^{-\mathrm{x}^{2} / 2}$. The value of N that normalizes the function $\psi(\mathrm{x})$ is: $\left(\right.$ Given $\left.\int_{-\infty}^{+\infty} \mathrm{x}^{2 \mathrm{n}} \mathrm{e}^{-\mathrm{x}^{2}} \mathrm{dx}=\frac{1 \cdot 3 \cdot 5 \cdots (2 \mathrm{n}-1)}{2^{\mathrm{n}}} \sqrt{\pi}\right)$