# Gamma Under Sum

Calculus Level 5

$S_x = \large \sum_{k = 0}^{\infty} \left [ {(-1)^k \times k \times 7^k \times \dfrac{x^{k+1}}{(e^x -1) \times \Gamma(k+2)}} \right ]$

Given an equation above, let $I = \int_{0}^{\infty} {S_x \, dx}$

If $$I$$ can also be expressed as $I = \int_{0}^{1}{\dfrac{t^A}{t-1} (\ln(t))^B \, dt},$

find $$A+B$$.

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