\int_{0}^{\infty}
\frac{e^{-x^2}}{1 + \dfrac{x^2}{a^2}} \, dx
= \frac{\sqrt{\pi}\,a}{2}
\left[
1 - \frac{1}{\sqrt{1+a^2}}
\right]
源码：
[math]
\int_{0}^{\infty}
\frac{e^{-x^2}}{1 + \dfrac{x^2}{a^2}} \, dx
= \frac{\sqrt{\pi}\,a}{2}
\left[
1 - \frac{1}{\sqrt{1+a^2}}
\right]
[/math]