<math>\int_0^\infty e^{-ax^2}\,\mathrm dx = \frac{1}{2}\frac{\sqrt{\pi}}{a}</math>

<math>\int_{-\infty}^\infty e^{-ax^2}\,\mathrm dx = \frac{\sqrt{\pi}}{a}</math>

Integration By Parts: <math>\int{u}{dv}\,\mathrm = uv-\int{v}{du}</math>