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I want to find the derivative of factorial function f(x)=x! and i found this integral,

[tex]f(x)=x!=\int_{0}^{\infty}e^{-t}t^xdt[/tex] when i take derivative of this

[tex]\frac{d}{dx}f(x)=\frac{d}{dx}\int_{0}^{\infty}e^{-t}t^xdt=\int_{0}^{\infty}e^{-t}t^xlnxdx[/tex]

How do i find this integral? Please help me. Thanks.

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# Derivative of x!

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