# A calculus problem by Sal Gard

Calculus Level pending

Evaluate integral from 0 to infinity p(x)-x/ln(x) dx. If it is in the form a-e^-b, find a^(2b). Note: p(x) is the prime counting function.

Moderator's edit:

$\large \int_0^\infty \dfrac{p(x) - x}{\ln x} \, dx$

Let $$p(x)$$ denote the prime counting function, that $$p(x)$$ denotes the function counting the number of prime numbers less than or equal to some real number $$x$$.

If the integral above is equal to $$a - e^{-b}$$, where $$a$$ and $$b$$ are integers, find $$a^{2b}$$.

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