I_2 = \int_{0}^{\infty}x^2 e^{-ax^2} \ dx = \frac{1}{4} \sqrt{\frac{\pi}{a^3}}

I_4 = \int_{0}^{\infty}x^4 e^{-ax^2} \ dx = \frac{3}{8} \sqrt{\frac{\pi}{a^5}}