Integral of a defined function-

Calculus Level 4

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

f(x)=r=0xr2 (xr).f(x) = \displaystyle\sum_{r=0}^x r^{2}~\dbinom{x}{r}.

Find the value of

2401f(x)2xdx. 24 \displaystyle\int_0^{1} \dfrac{f(x)}{2^{x}} dx.

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