Integrate using what!

Calculus Level 5

\[\large{\displaystyle \int^{\infty}_{0} x^{9} \frac{e^{x}(11e^x-11e^{2x}+e^{3x}-1)}{(e^x+1)^{5}} dx}\]

The value of above integral is equal to \(\large{\frac{A}{B} \pi^{C}}\) where \(A,B,C\in \mathbb Z\) and \(A,B\) are co-prime integers.

Find \(A\times(B+C)\)

Original problem

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