# 2407-2406-0-e-x-x-2406-dx-How-evaluate-e-x-x-2406-dx-

Question Number 10994 by geovane10math last updated on 06/Mar/17
$$\Gamma\left(\mathrm{2407}\right)\:=\:\left(\mathrm{2406}\right)!\:=\:\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} {x}^{\mathrm{2406}} \:\mathrm{dx} \\$$$$\mathrm{How}\:\mathrm{evaluate}\:\int{e}^{−{x}} {x}^{\mathrm{2406}} \:\mathrm{dx}\:??? \\$$
Commented by FilupS last updated on 06/Mar/17
$$\int{uv}'{dx}={uv}−\int{u}'{vdx} \\$$
Commented by FilupS last updated on 06/Mar/17
$${u}=\:{x}^{\mathrm{2406}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{v}'={e}^{−{x}} \\$$$${u}'=\mathrm{2406}{x}^{\mathrm{2405}} \:\:\:\:\:\:\:\:\:\:\:{v}\:=−{e}^{−{x}} \\$$$$\int{e}^{−{x}} {x}^{\mathrm{2406}} \:{dx}=\left[−{x}^{\mathrm{2406}} {e}^{−{x}} −\mathrm{2406}\int−{e}^{−{x}} {x}^{\mathrm{2405}} {dx}\right]_{\mathrm{0}} ^{\infty} \\$$$$\mathrm{repeat}\:\mathrm{process}\:\mathrm{for}\:\mathrm{all}\:\mathrm{2406}\:\mathrm{integrals} \\$$
Commented by geovane10math last updated on 06/Mar/17
$$\mathrm{Thanks}! \\$$