Empress Elisabeth of Austria did maths .

She is famous for this integral :

$$\int_{0}^{\pi}Si(x)Si(x)dx$$

Wich is an unsolved problem .(lol)

Well I like maths at a amateur level and also Monty Python .My god in music is JS Bach played by Glenn Gould.I dislike philosophy .Now...I sleep.

Try to show for $0<x\leq 1$ :

$$\frac{\ln\left(x^{\frac{29}{50}x^{\int_{0}^{1}x^{-x}dx}}+1\right)}{\ln\left(2\right)}\ge x!$$

Try to show :

$$\int_{1}^{\infty}x^{\frac{x^{\frac{1}{x}}\left(\pi-e-x!\right)}{x^{\frac{1}{x}}+2-\frac{2}{\sqrt{3}}}}dx<1$$