Show that $\int_0^1 e^{-\frac{1}{x}}dx > \frac{1}{4}e^{-\frac{4}{3}}$

I wanted to prove that some integral is bounded by a number. After some steps I got that I need to show this: $\int_0^1 e^{-\frac{1}{x}}dx > \frac{1}{4}e^{-\frac{4}{3}}$. But I can't find a good function to compare with $e^{-\frac{1}{x}}$ in order to show this inequality.