# Limit without a closed form

Calculus Level 4

$\large f(x)=\dfrac1{x^2}\int_x^{x+6}\sqrt{5t^4+1}\,dt$

If $$\displaystyle \lim_{x\to\infty} f(x) = \alpha \sqrt{\beta}$$, where $$\alpha$$ and $$\beta$$ are positive integers with $$\beta$$ square-free, write your answer as $$\alpha + \beta$$.

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