My, what large powers you have!

Calculus Level 3

The integral of \((x+1)(\frac{x}{2} - 1)^{10}\) with respect to \(x\) can be expressed as \(\frac{\alpha}{\beta} (\frac{x}{2}-1)^\gamma + \frac{\delta}{\epsilon} (\frac{x}{2}-1)^\omega + c\) where \(c\) is the arbitrary constant. \(gcd (\alpha, \beta) = gcd (\delta, \epsilon) =1\) and \(\gamma > \omega\).

All I need you to add up is \(\delta\) and \(\epsilon\). What is the answer???

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