Log o' Gamma

Calculus Level 5

23ln(Γ(x))dx \large \int_{2}^{3} \ln(\Gamma(x))\, dx If the result of the integral above can be expressed in the form aclnc+bclnπc\large \frac{a}{c}\ln{c}+\frac{b}{c}\ln{\pi}-c where a,b\large a,b and c\large c are positive coprime integers. Find the value of a+b+c\large a+b+c.

Note that Γ(x)\Gamma(x) is the Gamma Function.

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