integration - Integral of $x^2 \exp(-ax^2)$ using the gamma function? - Mathematics Stack Exchan
I'm struggling with this integral: $$\int_{-\infty}^{\infty}x^{2}e^{-ax^{2}}dx = \frac{\sqrt{\pi}}{2a^{3/2}}$$ Is there a way to do this integration without using integration by parts and then explicitly relying on the Gaussian int...