Who's up to the challenge? 2

Calculus Level 5

\[ \large \int_0^\infty \dfrac{x^9 \ln x}{e^x} \, dx \]

If the above integral can be expressed as \[144(B -C\gamma), \] where \(B\) and \(C\) are integers, find \(B+C+144 \).

Notation: \(\gamma\) denotes the Euler-Mascheroni constant \[ \displaystyle \gamma = \lim_{n\to\infty} \left( - \ln n + \sum_{k=1}^n \dfrac1k \right) \approx 0.5772 .\]


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