# 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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