\[\begin{array}{l} I + I = \int\limits_0^1 {\left( {\ln \Gamma \left( x \right) + \ln \Gamma \left( {1 - x} \right)} \right)dx} = \hfill \\ \int\limits_0^1 {\ln \left( {\Gamma \left( x \right)\Gamma \left( {1 - x} \right)} \right)dx} = \int\limits_0^1 {\ln \frac{\pi }{{\sin \left( {\pi x} \right)}}dx} = \ln \left( {2\pi } \right). \hfill \\ \end{array} \]

\[\ln \sqrt {2\pi } \]