$latex boxed {displaystyleint_{0}^{1}{x^{x}dx }= frac {1}{1^1} – frac {1}{2^2} +frac {1}{3^3} – frac {1}{4^4} + frac {1}{5^5} +…}$

$latex boxed {displaystyleint_{0}^{1}{x^{-x}dx }= frac {1}{1^1} +frac {1}{2^2} +frac {1}{3^3} + frac {1}{4^4} + frac {1}{5^5} + …}$