# Limit of a Definite Integral #2

Calculus Level 5

$\large f(x) = \frac2{e^x - e^{-x}} \left( 1 + \int_1^x f(t) \, dt \right)$

Suppose a function $$f$$ defined on $$x>0$$ satisfy the equation above, find the value of $$\displaystyle \left \lfloor 100 \cdot \lim_{a\to\infty} \int_{\frac1a}^a f(t) \, dt \right \rfloor$$.

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