# Proofs of $\sum_{n=1}^\infty \frac{1}{n^n}=\int_0^1 \frac{1}{x^x}dx$ [duplicate]

Prove that $\sum_{n=1}^\infty \frac{1}{n^n}=\int_0^1 \frac{1}{x^x}dx$. This comes from this question Evaluate $\sum_0^\infty \frac{1}{n^n}$.