Neat expressions that equal 1 I would like to see beautiful and elegant expressions involving elementary and non-elementary functions, transcendental numbers, etc. that equal 1. 
Be creative!

Because any proper probability distribution must integrate to one, there can be a host of them. Here are two such:
$$
\large\int_{-\infty}^{\infty}\frac{1}{\pi(1+x^2)}dx\\
\large\int_{0}^{\infty}\left[\frac{\lambda}{2 \pi x^3}\right]^{\frac{1}{2}}e^{\frac{-\lambda (x-\mu)^2}{2 \mu^2 x}}dx\\
$$
