Another Logarithm Problem.(14)

Calculus Level 5

\[\large \displaystyle \int_1^\infty \left(\frac{\ln x}{x} \right)^{2011} dx = \frac{b!}{a^c} \]

If the above equation is true, where \(a\), \(b\), and \(c\) are positive integers, find \(a + b + c\).

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