Question

$\huge\displaystyle \sf \red{\int_{0}^{1} (x!)^{dx} }$​

Answer 1

$\displaystyle \sf \red{\int_{0}^{1} (x!)^{dx} }$

$\displaystyle \sf \red{\int_{0}^{1} ( \Gamma(x + 1))^{dx} }$

$\displaystyle \sf \red{\prod^{1}_{0} {{}^{} ( \Gamma(x + 1))^{dx} }}$

$\displaystyle \sf \red{\int_{p}^{} ( \Gamma(x + 1))^{dx} }$

$\displaystyle \sf \red{exp \bigg(\int_{0}^{1} ln ( \Gamma(x + 1) \bigg)^{}dx }$

$\displaystyle \sf \red{exp \bigg({}^{} ln \bigg( \frac{ \sqrt{2\pi} }{e} \bigg) \bigg)^{} }$

$\displaystyle \sf \red{ \frac{ \sqrt{2\pi} }{e} }$