Let $F:[3,5] \to R$ be a twice differentiable function on (3, 5) such that $F(x) = {e^{ - x}}\int\limits_3^x {(3{t^2} + 2t + 4F'(t))dt} $. If $F'(4) = {{\alpha {e^\beta } - 224} \over {{{({e^\beta } - 4)}^2}}}$, then $\alpha$ + $\beta$ is equal to _______________.

Question

Let $F:[3,5] \to R$ be a twice differentiable function on (3, 5) such that

$F(x) = {e^{ - x}}\int\limits_3^x {(3{t^2} + 2t + 4F'(t))dt} $. If $F'(4) = {{\alpha {e^\beta } - 224} \over {{{({e^\beta } - 4)}^2}}}$, then $\alpha$ + $\beta$ is equal to _______________.

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