Question Number 113708 by Rasikh last updated on 15/Sep/20 | ||
$$\:\:\:\:\:\int\mathrm{x}^{\mathrm{x}} \:\mathrm{dx}\:=?\:\: \\ $$ | ||
Commented by Dwaipayan Shikari last updated on 14/Sep/20 | ||
$${Q}\:\mathrm{111558} \\ $$ | ||
Answered by bobhans last updated on 15/Sep/20 | ||
$$\int\:\mathrm{x}^{\mathrm{x}} \:\mathrm{dx}\:=\:−\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{n}\right)^{−\mathrm{n}} }{\left(\mathrm{n}−\mathrm{1}\right)!}\:\Gamma\left(\mathrm{n},−\mathrm{n}\:\mathrm{ln}\:\mathrm{x}\right) \\ $$ | ||