Integral of a defined function-

Calculus Level 4

Let a function \(f(x)\) be defined as:

\[f(x) = \displaystyle\sum_{r=0}^x r^{2}~\dbinom{x}{r}.\]

Find the value of

\[ 24 \displaystyle\int_0^{1} \dfrac{f(x)}{2^{x}} dx.\]

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