A beautiful function

Calculus Level 4

01ln(Γ(x))dx \large \int_0^1 \ln ( \Gamma(x) ) \, dx

If the value of the integral above is equal to ln(Aπ)A \dfrac{ \ln(A \pi)}A

for some constant AA, find AA.

Notation: Γ() \Gamma(\cdot) denotes the gamma function.

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