  We demonstrate high accuracy calculations for the HeH$^+$ molecule using
newly developed analytic formulas for two-center two-electron integrals with
exponential functions. The Born-Oppenheimer potential for the ground electronic
$^1\Sigma^+$ state is obtained in the range of 0.1 -- 60 au with precision of
about $10^{-12}$ au. As an example at the equilibrium distance $r=1.463\,283$
au the Born-Oppenheimer potential amounts to $-2.978\,708\,310\,771(1)$.
Obtained results lay the ground for theoretical predictions in HeH$^+$ with
spectroscopic precision.
