Calculus Level 5

$\lim_{x \to \infty} \frac{1}{x}\int_{0}^{x} \pi (t) - \frac{t}{\ln t}dt = a- e^b$

If $$a$$ and $$b$$ are integers, then what is $$a - b?$$

Note: $$\pi (x)$$ is the prime counting function.

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