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Question Number 113708 by Rasikh last updated on 15/Sep/20

     ∫x^x  dx =?

$$\:\:\:\:\:\int\mathrm{x}^{\mathrm{x}} \:\mathrm{dx}\:=?\:\: \\ $$

Commented by Dwaipayan Shikari last updated on 14/Sep/20

Q 111558

$${Q}\:\mathrm{111558} \\ $$

Answered by bobhans last updated on 15/Sep/20

∫ x^x  dx = −Σ_(n=1) ^∞ (((−n)^(−n) )/((n−1)!)) Γ(n,−n ln x)

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

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