Integral and Gamma Function (2)

Calculus Level 4

01(lnΓ(x))sin(πx) dx=1π(1+lnπA)\large \int_0^1(\ln\Gamma(x))\sin(\pi x)\ dx=\frac1\pi\left(1+\ln{\frac\pi A}\right)

Find AA.

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


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