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
$$\int\:\mathrm{x}^{\mathrm{x}} \:\mathrm{dx}\:=\:−\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{n}\right)^{−\mathrm{n}} }{\left(\mathrm{n}−\mathrm{1}\right)!}\:\Gamma\left(\mathrm{n},−\mathrm{n}\:\mathrm{ln}\:\mathrm{x}\right) \\ $$