Calculus Madness

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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