May be too lengthy 2

Calculus Level 5

\[\large{\displaystyle \int ^{1}_{0} \arctan(x) \left( (\ln x)^3+3 (\ln x)^2 \right)dx= \frac{A}{B} \pi^{C}}\]

where \(A,B,C\) are positive integers and \(A,B\) being co-prime.

Find \(A+B+C\)

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