Question Number 9201 by geovane10math last updated on 22/Nov/16
$$\int{x}!\:{dx}\:=\:? \\ $$$$ \\ $$
Commented by FilupSmith last updated on 23/Nov/16
$$\Gamma\left({x}\right)=\left({x}−\mathrm{1}\right)! \\ $$$$\psi\left({x}\right)=\frac{\Gamma'\left({x}\right)}{\Gamma\left({x}\right)} \\ $$$$\: \\ $$$$\int\left({x}!\right){dx}=\int\:\frac{\Gamma'\left({x}+\mathrm{1}\right)}{\psi\left({x}+\mathrm{1}\right)}{dx} \\ $$
Commented by FilupSmith last updated on 23/Nov/16
$$\mathrm{I}\:\mathrm{dont}\:\mathrm{think}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{simple}\:\mathrm{solution} \\ $$
Commented by 123456 last updated on 24/Nov/16
$${x}!=\underset{\mathrm{0}} {\overset{\infty} {\int}}{t}^{{x}} {e}^{−{t}} {dt} \\ $$