Integral in Prime counting function

147 Views Asked by At

I've come across on another stack exchange question somewhere that gave a definition for the integral that appears in Riemann's prime counting formula. The integral in question is $$\int_{x^{1/n}}^\infty\frac{1}{t(t^2-1)\ln(t)}dt$$ and if I recall, it was defined in terms of the Riemann function $R(x)$ and/or $\mu(x)$. Could someone help give the definition of this integral?